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Curriculum vitae of Francesco Altomare

Francesco Altomare was born on May 18th, 1951, in Giovinazzo  (Bari, Italy). He graduated in Mathematics from the University  of  Bari  in 1975. He was a senior research fellow from  1975  until  1978  at  the Institute of Mathematical Analysis of the University of Bari. From 1978 until 1985 and then until 1987 he has  been  assistant professor and associated professor at the Faculty of  Sciences  of  the University of Bari. He became  a  professor  at  the  Faculty  of  Sciences  of  the University of Basilicata (Potenza) in 1987 and in 1990 he  has  held  a professorship at the University of Bari were he is currently employed.

He served as

  • Director of the Institute  of  Mathematics  at  the University of Basilicata from 1987 to  1990. 
  •  Director  of  the Graduate School in Mathematics at the University of Bari from  1993  to 1995.
  • Head of the  Interuniversity  Department  of Mathematics of the University and the Polytechnic of Bari from 1997 to 1999 .
  • Coordinator of the Ph.D. School in Mathematics of the University of Bari from 1999 to 2003.
  • From 2012 he is Head of the Department of Mathematics of the University of Bari
  • For the period 2012 – 2015 he has been elected as a member of the Academic Senate of the University of Bari.

He is member of the Scientific Committee of Italian Mathematical Union and he is a member of the European Mathematical Society.

 

Research activities

 

The main areas of the scientific interests of Francesco Altomare are

  • Real and Functional Analysis (Choquet representation theory, Choquet boundaries, continuous function spaces, function algebras and Banach algebras, locally convex vector lattices, positive linear forms and applications to abstract Potential Theory and Harmonic Analysis.

 

  • Operator  Theory (Positive operators, semigroups of operators, differential operators  and applications to evolution equations)
  • Approximation Theory (Korovkin-type approximation theory, positive approximation processes, approximation of semigroups by means of positive operators).

More recently his researches are concerned with the Korovkin-type approximation theory in locally convex vector lattices of continuous functions on locally compact spaces, Stone-Weierstrass type theorems, asymptotic formulae for positive linear operators, saturation class as well as with the study of several sequences of positive linear operators associated with continuous selections of Borel measures (on a real interval or on a convex subset  of some Banch space), the relevant degenerate differential operators and positive semigroups generated by them and their Favard class.

The main results of the above-mentioned researches are documented in about 70  papers published in scientific journals, conference proceedings and special issues as well as in the monograph

Korovkin-type approximation theory and  its applications, de Gruyter Series  Studies  in  Mathematics,  17,  W.  de Gruyter & Co. Publ. Comp. Berlin, New York,  1994.

written jointly with M. Campiti.

 

Visitor activities

 

Francesco Altomare was a research visitor at the Universities of Paris VI (1980 and 1981), Tübingen(1983) and Münster (1985). In  1985 he also awarded a NATO research grant. On 2004 he spent a research period at the Mathematical  Institute of Oberwolfach under the RiP program.

He was  invited  to  deliver  lectures  and  postgraduate  short courses and to develop joint researches at several italian and  foreign universities (Napoli,  Lecce, Cosenza,  Potenza, Roma, Milano, Bologna, Trieste, Salerno, Palermo Perugia, Sofia, Annaba,  Erlangen,  Passau,  Valencia,  Praga, Paseky, Siegen, Vienna).

 

Conferences

 

He also participated  in  about fifty international  meetings  as invited  speaker  (Italy,  Germany,  U.S.A.,  Brasil,  Rumania,  Spain, Hungary, Czech Republic, Russia, Taiwan, Austria ). Among the more recent ones we quote:

1) International Conference on Mathematical Analysis and its Applications, Kaohsiung (Taiwan), 17-21 Gennaio, 2000 (Transition semigroups on weighted function spaces).

 

2) Colloquium on Analysis, Wien, March 10-11 , 2000, Lototsky – Schnabl operators and Feller Semigroups).

 

3) 3rd International Conference on Differential Equations in Banach Spaces, Bologna, July 3-7, 2000 (Some remarks on second order differential operators on weighted function spaces).

 

4) TULKA Conference on Semigroups and Evolution Equations, Blaubeuren, Germany, June 13-17, 2001 (On a class of evolution equations of interest in Mathematical Finance).

 

5) 1st Intern. Workshop on Functional Analitic Methods in Economics and Finance, Diamante (CS), June 28-30, 2001 (Degenerate evolution problems and related Markov processes occurring in Mathematical Finance).

 

6) Convegno INDAM su “Evolution equations and semigroups”, Cortona, 7-12 aprile 2002, (Positive semigroups on weighted spaces of continuous functions and Markov processes).

 

7) T. Popoviciu Itinerant Seminar on Functional Equations, Approximation and Convexity, May 22-26, 2002, Cluj-Napoca, Romania, (Methods of measure theory for approximation problems by positive linear operators).

 

8) 5th Congress of Romanian Mathematicians, June 22-28, 2003, Piteşti, Romania (Affine projections on adapted subalgebras).

 

9) 4th International Conference on Constructive Approximation, Witten – Bommerholz, Germany, 15 – 20 febbraio, 2004, (On some simple methods to construct positive approximation processes satisfying prescribed asymptotic formulae).

10) Fejér – Riesz Conference, Eger, Hungary, June 8 – 14, 2005, (Locally Convex Riesz Spaces and generalized affine functions).

 

11) 2nd International Workshop on Functional Analysis Methods in Economics and Finance, Cetraro (CS), Italy, July 7-9, 2005, (Positive operators and initial-boundary problems associated with the Black-Scholes equation).

 

12) International Conference on Numerical Analysis and Approximation Theory, Cluj-Napoca, Romania, July 5 – 8, 2006 (Continuous selections of Borel measures and positive approximation processes).

 

13) 2nd International Symposium on Banach and Function Spaces, Kitakyushu, Japan, September 14 – 17, 2006 (On a class of vector lattices of functions spaces and related approximation/density problems).

 

14) Autumn Congress of the Mathematical Society of Japapn 2006, Osaka, Japan, September 19 – 22, 2006 (Positive operators associated with continuous selections of Borel measures and their limit Feller semigroups).

 

15) VIII International Meeting on Approximation Theory, Ubeda, Spain, November 7 – 11, 2007 (Asymptotic formulae for Bernstein operators and for other classes of positive linear operators).

 

16) Functional Analysis: Methods and Applications, FAMA 2008, Amantea, Cosenza, Italy, June 4 – 7, 2008 (Asymptotic formulae for positive linear operators and smoothness).

 

17) Conferenze Scientifiche di Analisi Matematica. Omaggio a Calogero Vinti. Perugia, 13 dicembre  2008. (Operatori ellittici degeneri, semigruppi di Feller e loro approssimazione tramite operatori positivi).

 

18)  1st Jaen Conference on Approximation Theory, Computer Aided Geometric Design, Numerical Methods and Applications, Ubeda, Spain, July 4-9, 2010 (Asymptotic formulae and positive semigroups of operators).

 

19)  2nd International Conference on Numerical Analysis and Approximation Theory (NAAT 2010), Cluj-Napoca, Romania, September 23-26, 2010 (Approximation problems by positive linear operators in function spaces on unbounded domains).

 

Research fellows and Ph.D. students

He supervised the scientific activities of seven undergraduate and postgraduate research fellows and the following six Ph.D. students:

  1. Sabrina Diomede, University of Napoli, 1998 – 2002.

Ph.D. thesis: Positive approximation processes on continuous function spaces.

 

  1. Mirella Cappelletti Montano, University of Bari, 2000 – 2003.

Ph.D. thesis: Approximation problems for positive operators on adapted spaces.

 

  1. Rachida Amiar, University of Annaba (Algeria), 1998 – 2005.

Ph.D. thesis Méthode des opérateurs positifs pour l’étude des equations de diffusion.

4. Vita Leonessa, University of Bari, 2002 –  2005.

Ph.D. thesis: Positive operators associated with continuous selections of Borel measures.

 

 

     5. Sabina Milella, University of Bari, 2002 – 2005.

Ph.D. thesis: Evolution equations on real intervals, semigroups and their approximation.

     6. Graziana Musceo, University of  Bari , 2003 – 2006.

Ph.D. thesis: Positive semigroups  in weighted spaces of continuous functions.

 

Journals editorial activities

 

He contributes to Mathematical Reviews as a reviewer and acts as a referee for several national and international journals.

Since 2004 he is the founding Editor-in-Chief of the international journal Mediterranean Journal of Mathematics.

He is a member of  the Editorial Board of the following journals:

· Conferenze del Seminario di Matematica dell’Università di Bari (from 1990 to 2003),  

· Revue d’Analyse Numèrique et de Thèorie de l’Approximation  (since 1998),

· Mathematical Reports (since 2000),

· Journal of Interdisciplinary Mathematics (since 2004)

· Journal of Applied Functional Analysis (since 2004).

· Numerical Functional Analysis and Optimization (since 2008),

· Bollettino dell’Unione Matematica Italiana (since 2008).

· Studia Mathematica Universitatis Babeş-Bolyai (since 2009).

· The Journal of the Indian Academy of Mathematics (since 2009).

 

Research centers

 

Francesco Altomare is on the Scientific Committee of the  Center for Studies on Functional Analysis and Approximation Theory (University of Basilicata -  Potenza)  and  on  the  Scientific  Committee  of  the Institute for Researches on Applied Mathematics of the National Council of Researches (Bari).

 

Research projects

 

He is or has been the co-ordinator of  the research projects

-  “Topological structures and functional analytic methods in operator theory”   financed  by  the  University  of  Bari from the year 1994 until now.

    - an interuniversity research project “Operator Methods for Evolution Equations and Approximation Problems” between the Universities of Bari and Lecce and the Polytechnic of Bari financed by the National Group for Mathematical Analysis, Probability and their Applications for the year 2002.

 

- “Positive Operators, Semigroups and Applications to Evolution Equations and Approximation Problems” financed by  the University of Bari for the years 2003-2004,

  • a national research project “Operator theory, Semigroups and Applications to Evolution Equations and Approximation Problems”  financed by the Italian Ministry for Education for the years 2003/04 – 2004/05 (PRIN-COFIN 2003).

- the project “Positive Operators, Evolution Equations and Approximation Problems” financed by the Italian Ministry for Education for the years 2003/04 – 2004/05 (FIRB 2004).

 

Conferences Organization  

       He  contributed   to   the   organization   of   the   following international  meetings  and  was  co-editor   of   the   corresponding proceedings:

  • “Trends  in  Functional  Analysis  and  Approximation   Theory”, Acquafredda di Maratea (September 11-16, 1989).
  • “ Recenti sviluppi  in  Analisi  Matematica  e  sue  Applicazioni  “, dedicated to Prof. Aquaro on occasion of his 70° birthday,  Bari (November 8-9, 1990).
  • “  2nd  International  Conference   on   Functional   Analysis and Approximation Theory “, Acquafredda di Maratea (PZ),  (September 14-19, 1992).
  • “  3rd  International  Conference   on   Functional   Analysis and Approximation Theory “, Acquafredda di Maratea (PZ),  (September 23-28, 1996).
  • “  4th   International  Conference   on   Functional   Analysis and Approximation Theory “, Acquafredda di Maratea (PZ),  (September 22-28,  2000).

·   Special Session on Semigroups of Operators and Applications during the 1st Joint              International Meeting AMS-UMI Pisa, Italy - June 12-16, 2002

·   International Summer School on “Operator Methods for Evolution Equations and Approximation Problems, Monopoli (Bari-Italy), September 15 – 22, 2002.

· “  5th   International  Conference   on   Functional   Analysis and Approximation Theory “, Acquafredda di Maratea (PZ),  (June 16 – 23, 2004).

  • International Conference for the Presentation of Mediterranean Journal of Mathematics, Bari, 21 – 22 gennaio 2005.

· International Conference on Functional Analysis and Operator Theory, Mondello (Palermo), 19-24  Sept. 2005

  • He has been the President of the Organizing Committee of the XVIII Congress of the Italian Mathematical Union, Bari, 24 – 29 settembre 2007.
  • 6th International  Conference   on   Functional   Analysis and Approximation Theory , Acquafredda di Maratea (PZ),  (September  24 –30,  2009).

 


Publications list of  Francesco Altomare

 

Monographs

 

[1] F.  Altomare  and  M.  Campiti,  Korovkin-type  Approximation Theory and its    Applications, de Gruyter Series  Studies  in Mathematics, 17, W. de Gruyter & Co. Publ. Comp., Berlin,  New York, 1994. MR 95g:41001.

 

[2] F. Altomare, Korovkin-type Theorems and Approximation by Positive Linear Operators, Surveys in Approximation Theory, Vol. 5, 2010, 92-164, free available online at http://www.math.technion.ac.il/sat/papers/13/, ISSN 1555-578X

 

Research articles

 

1977

 

[1] Proiettori  positivi,  famiglie  risolventi  e  problema   di Dirichlet, Ricerche di Matematica, Vol. XXXVI, 1977, fasc. 1°, 63-78. MR 58 # 30099

 

1978

 

[2] Operatori di Lion generalizzati e famiglie risolventi,  Boll. U.M.I. in (5), 15-B (1978), 60-79.

 

[3] Operatori di Lion sul prodotto di spazi compatti,  semigruppi di operatori positivi e problema di Dirichlet, Ricerche di Matematica, Vol. XXVIII, 1978, fasc. 1°, 33-58. MR 80d: 47048

 

1979

 

[4] Theoremes de convergence de type Korovkin relativement a une applications lineaire positive,  Boll.  U.M.I.  (5)  16-B (1979).MR 81d: 41028.

 

1980

 

[5] Teoremi di approssimazione di tipo Korovkin in spazi di funzioni, Rendiconti di Matematica, (3) 1980 Vol. 13, Serie VI, 409-429. MR 82h: 41029.

 

[6] Su alcuni aspetti della teoria dell'approssimazione  di  tipo Korovkin,  Quaderni  dell'Istituto  di   Analisi   Matematica  dell'Università di Bari, 1980.

 

[7] Quelques remarques sur les ensembles  de  Korovkin  dans  les espaces  des  fonctions  continues  complexes, Seminaire Initiation a l'Analyse, 20e année, 1980/81, n. 4, p. 12.    MR 83j: 41026

 

1981

 

[8]  Frontiéres abstraites et convergence de familles  filtrées  de formes linéaires sur les algébres de Banach commutatives, Séminaire Initiation a l'Analyse (G. Choquet, M. Rogalki,  J. Saint Raimond), 21e Année, 1981/82, n. 6, 16 p. ZBL 514-43032

 

 

1982

 

[9] (with C. Boccaccio) On Korovkin-type  theorems  in  spaces  of continuous complex valued functions, Boll. U.M.I. (6)  1-B  (1982), 75-86. MR 83j: 41028.

 

[10] On the Korovkin approximation theory  in  commutative  Banach algebras, Rendiconti di  Matematica,  (4)  1982,  Vol.  2, Serie VII, 755-767. MR 84g: 41019.

 

1983

 

[11]  (with R. Nagel)  Semigruppi di operatori positivi , Quaderni    del    Dipartimento    di    Matematica dell'Università di Bari, n. 2, 1983.

 

1984

 

[12]  On the universal convergence sets, Annali  di  Matematica Pura Appl., (IV) 1984, Vol. CXXXVIII, pp. 223-243.MR 86h: 41024.

 

[13] Korovkin closures in spaces of continuous  affine  functions, Semesterbericht Funktional Analysis,  Tubingen,  Winter  sem. 84/85.

 

1985

 

[14] Sur quelques problémes de probabilités du  type  aiguille  de Buffon, Pub. Inst. Stat. Univ. 30(1985), no. 1-2, 1-14.

 

1986

 

[15] Korovkin  closures  in  Banach  algebras,  Operator   Theory: Advances and Applications, Vol. 17, 35-42, Birkhauser  Verlag, Basel, 1986. MR 88g: 41019.

 

1987

 

[16] Nets of positive operators in  spaces  of  continuous  affine functions, Boll. Un. Mat. Ital. (7) 1-B (1987), 217-233. MR 88k: 46024.

 

[17] Korovkin-type theorems for positive functionals in spaces  of continuous affine functions, Rend. Circ. Mat. Palermo (2)  36 (1987), 167-181. MR 90c: 46035.

 

[18] Approximation  of  finitely  defined  operators  in  function spaces, Note Mat. 7 (1987), 211-229. MR 90i: 47029.

 

1989

 

[19] Positive linear forms and their determining  subspaces,  Ann. Math. Pura Appl. 154 (4) (1989), 243-258. MR 91d: 46003.

 

[20] Limit semigroups of  Bernstein-Schnabl  operators  associated with positive projections, Ann. Sc. Norm.  Sup.  Pisa,  Serie IV, (16) 2 (1989), 259-279. MR 91a: 47036.

 

[21] (with I. Raşa) Approximation  by  positive  operators  in  the space C(p)([a,b]), Anal. Numér. Théor. Approx. 18, 1  (1989), 1-11. MR 91i: 41018.

 

[22] On a sequence of Bernstein-Schnabl  operators  defined  on  a cylinder, Approximation Theory VI: Volume 1, C.K. Chui,  L.L. Schumaker and J.D. Wards (eds.),  pp.  5-8,  Academic  Press. N.Y., 1989.

 

[23] (with M.  Campiti)  A  bibliography  on  the  Korovkin   type Approximation Theory  (1952-1987),  Functional  Analysis  and Approximation, P.L. Papini Ed., pp. 34-79, Pitagora Editrice, Bologna 1989. MR 90m: 41001.

 

1991

 

[24] Convergence subspaces associated  with  discrete  measures,   Atti Sem. Mat. Fis. Univ.  Modena, 39 (1991), 473-486. MR 93 c: 28012.

 

[25]  Positive projections, approximation processes and  degenerate diffusion equations, Atti del Convegno  "Recenti sviluppi in Analisi Matematica e sue applicazioni",  dedicato al Prof. G. Aquaro in occasione del suo 70° compleanno, Bari, 8-9 Novembre 1990, Conf. Sem.  Mat. Univ. Bari,  241  (1991),  43-68. MR 93i: 41015.

 

[26] Lototsky-Schnabl operators on the unit  interval,C.R.Acad.Sci.Paris, t.313, S‚rie I, p.371-375, 1991, MR 92j: 41035.

 

[27] On  some  approximation  processes   and   their   associated parabolic  problems,  Rend.  Sem.  Mat.  Fis.  Univ.  Milano,  59(1991), 231-255. (1994).

 

1992

 

[28] Lototsky-Schnabl  operators  on   the   unit   interval   and degenerate diffusion equations, in: Progress in Functional Analysis ( K.D.Bierstedt, J.Bonet, J.Horvàth  and  M.Maestre Eds. ), Proceedings of the International Functional  Analysis Meeting on the occasion of the  60th  birthday  of  Professor M.Valdivia,   Peniscola,   Spain,   22-27   October ,1990,  North -Holland Math. Studies 170, pp. 259-277, North-Holland Publishing Co., Amsterdam,1992. MR 93e: 41034.

 

[29] Lototsky-Schnabl operators on compact convex sets  and  their associated   limit   semigroup, Mh. Math., 114, (1992), 1-13. MR 94c: 47044.

 

[30] (with S.  Romanelli)  On  some  classes  of  Lototsky-Schnabl operators, Note Mat. 12 (1992), 1-13.

 

 

 

1994

 

[31] Approximation theory and evolution equations,  Proceedings of the meeting "Swabian-Apulian meeting  on  operator  semigroups and evolution equations", Ruvo di Puglia (Italy), March 28  - April 2, 1994, Conf. Sem.  Mat. Univ. Bari, 258(1994), 1-26.

 

1995

 

[32]  Approximation theory  methods  for  the  study  of  diffusion equations, Approximation Theory (Witten, 1995), 9 -  26, Math. Res., 86, Akademie - Verlag, Berlin, 1995. MR 96m:41032.

 

1996

 

[33] (with I. Carbone) On  a  new  sequence  of  positive  linear operators on unbounded intervals, Proceedings of the Workshop "Functional Analysis:  Methods  and  Applications"  (Cosenza, 1995) Rend. Circ. Mat. Palermo (2) Suppl. No. 40 (1996),23-36. MR 97g:41037.

 

1997

 

[34] (with A. Attalienti) Forward diffusion equations and  positive operators, Math. Z. 225 (1997), 211 -229. MR 98i:41029.

 

[35] (with I. Carbone) On some  degenerate  differential  operators on weighted function spaces, J. Math. Anal.  Appl.  213(1997), 308 - 333. MR 98i:47036

 

[36] On some sequences of positive linear operators  on  unbounded intervals, Approximation and Optimization, Vol.1 (Cluj -  Napoca, 1996 ) 1 - 16, Transilvania, Cluj-Napoca, 1997. MR 98k:41040.

 

1998

 

[37] (with I.  Raşa)  Towards  a  characterization  of  a   class   of differential operators associated with positive projection,  Atti Sem. Mat. Fis. Univ. Modena,  Supplemento  al  n.  XLVI,  (1998), 3-38. MR 99h:35072.

 

[38] (with I. Raşa) On a Class  of  Differential  Operators  Associated with Positive Projections, Rend. Circ. Mat.  Palermo  (2)  Suppl. 56(1998), 79 - 89.

 

1999

 

[39] (with I. Raşa) Feller Semigroups, Bernstein - type  Operators  and Generalized  Convexity  Associated  with  Positive   Projections, New  Developments  in  Approximation  Theory (Dortmund 1998), 9-32, Internat. Ser. Numer. Math., 132,   Birkhauser , Basel, 1999. MR 2000m:41036

 

[40] (with E. Mangino)  On  a  generalization  of  Baskakov  operators, Rev. Roumaine Math. Pures Appl., 44(1999), 5-6, 683-705. MR 2002c: 41033.

 

2000

 

[41] Degenerate  evolution  equations  on  weighted  function  spaces, Markov processes and positive operators, Séminaire de la Théorie de la Meilleure Approximation, Convexité et Optimization, 1960 – 2000, Editura SRIMA, Cluj-Napoca, Romania, 2000, pp.29-58.

 

2001

 

[42] (with E. Mangino) On a class of elliptic - parabolic equations  on unbounded intervals, Positivity, 5(2001), 239-257. MR 2002d: 35082.

 

[43] (with I. Carbone) Markov  processes  and  diffusion  equations  on unbounded intervals, Taiwanese J. of Math., 5 (2001), 1, 141-167. MR 2001m: 60171.

 

[44] (with S. Diomede) Contractive Korovkin subsets in weighted  spaces of continuous functions, Rend. Circ. Mat. Palermo, Serie II, 50 (2001), pp. 547-568. MR 2002j:41021.

 

2002

 

[45] (with A. Attalienti) Degenerate  evolution  equations in weighted continuous function spaces, Markov processes and the Black-Scholes equation - Part I, Result. Math. 42(2002), 193-211. MR2003k :34103

 

[46] (with A. Attalienti) Degenerate  evolution  equations in weighted continuous function spaces, Markov processes and the Black-Scholes equation - Part II, Result. Math. 42(2002), 212-228. MR 2003k:34104

 

[47] (with R. Amiar) Asymptotic formulae for positive linear operators, Mathematica Balkanica, New Series, 16(2002), Fasc. 1-4, 283-304. MR 2003k: 41033.

 

 [48] (with S. Diomede) Methods of measure theory for approximation problems by positive linear operators,  Proceedings of the T. Popoviciu Itinerant Seminar, E. Popoviciu Ed., 31-51, Editura SRIMA, Cluj-Napoca, Romania, 2002.

 

 

2003

 

[49] (with S. Diomede) Positive operators and approximation in function spaces on completely regular spaces,  Int. J. of Math. and Math. Sci. 61(2003), 3841-3871. MR 2004m: 41027

 

 

 

 

2005

 

[50] (with I. Raşa) On some classes of diffusion equations and related approximation problems, trends and Applications in Constructive Approximation, (Eds) M.G de Bruin, D.H. Mache & J. Szabados,  Internat. Series of Numerical Mathematics, Vol 151 (2005), Birkhäuser Verlag, Basel, pp. 13 – 26.

 

[51] (with I. Raşa) On a Class of Exponential-type Operators and their Limit Semigroups, J. of Approx. Theory 135(2005), no. 2, 258 - 275.

 

[52] (with R. Amiar) Approximation by Positive Operators of the C0-Semigroups Associated with One-Dimensional Diffusion Equations - Part I, Numer. Func. Anal. Optim. 26 (2005), 1, 1 - 16.

 

[53] (with R. Amiar) Approximation by Positive Operators of the C0-Semigroups Associated with One-Dimensional Diffusion Equations - Part II, Numer. Func. Anal. Optim. 26 (2005), 1, 16 – 33, Corrigendum: Numer. Func. Anal. Optim. 27 (2006), 3-4, 497-498.

 

[54] (with M. Cappelletti Montano) Affine projections on adapted subalgebras of continuous functions, Positivity 9 (2005), no. 4, 625 - 643.

 

[55] (with M. Cappelletti Montano) Regular vector lattices of continuous functions and Korovkin-type theorems — Part I,  Studia Math. 171 (3) (2005), 239 – 260.

 

[56] (with S. Diomede) Asymptotic formulae for positive linear operators on convex sets of Banach spaces, J. of Concrete and Appl. Analysis, 3(2005), no. 4, 413-435..

 

2006

 

[57] (with M. Cappelletti Montano) Regular vector lattices of continuous functions and Korovkin-type theorems — Part II, Studia Math. 172 (1) (2006), 69 – 90.

 

[58] (with V. Leonessa)  On a sequence of positive linear operators associated with a continuous selection of Borel measures, Mediterr. J. Math., 3(2006), no. 3 - 4, 363 - 382.

 

[59] (with V. Leonessa e S. Milella) Continuous selections of Borel measures and Bernstein-Schnabl operators, Proc. Intern. Conf. Numer. Anal. and Approx. Th.(NAAT 2006), Cluj-Napoca (Romania), July 5-8, 2006.

 

 

2007

 

[60] (with M. Cappelletti Montano) On some density theorems in regular vector lattices of continuous functions, Collect. Math. 58, 2 (2007), 131 – 149.

 

[61] (with V. Leonessa) Continuous selections of Borel measures, positive operators and degenerate evolution problems, Rev. Anal. Numer. Theor. Approx., 36(2007), no. 1, 9 –23.

 

2008

 

[62] (with M. Cappelletti Montano) On a class of locally convex vector lattices of continuous function spaces and related approximation/density problems, Proc. Intern. Symp. on Banach and Function Spaces II (ISBFS 2006), Kitakyushu (Japan), 14 – 17 September, 2006, Yokohama Publishers, Yokohama, 2008, pp. 25 – 50.

 

[63] (with G. Musceo) Markov processes and positive semigroups on some classes of weighted continuous function spaces, Rend. Circ. Mat. Palermo, 57 (2008), 61 - 82.

 

[64] (with S. Milella) Integral-type operators on continuous function spaces on the real line, J. of Approx. Theory 152 (2008), 107 - 124.

 

[65] (with V. Leonessa and I. Raşa)  On Bernstein-Schnabl operators on the unit interval, J. for Anal. and its Appl. 27(2008)3, 353 – 379.

 

[66] (with G. Musceo) Positive semigroups generated by degenerate second-order differential operators, Funkcialaj Ekvacioj, 51(2008), 431 - 458.

 

[67] (with S. Milella) On a sequence of integral operators on weighted Lp spaces, Analysis Math. 34(2008), 237 – 259.

 

2009

 

[68] Asymptotic formulae for Bernstein-Schnabl operators and smoothness, Bollettino U.M.I., (9) II (2009), 135 – 150, Corrigendum: Bollettino U.M.I., (9) IV (2011), 259 – 262.

 

[69] (with S. Milella) On the C0-semigroups generated by second-order differential operators on the real line, Taiwanese J. Math., 13(2009), no. 1, 25-46.

 

 [70] (with V. Leonessa and S. Milella) Cores for second-order differential operators on real intervals, Commun. Appl. Analysis, 13(2009), no. 4, 477-496.

 

[71] (with V. Leonessa and S. Milella) Bernstein-Schnabl operators on noncompact real intervals, Jaén J. Approx., 1(2) (2009), 223 - 256.

 

[72] (with V. Leonessa) An invitation to the study of evolution equations by means of positive linear operators, Lecture Notes of Seminario Interdisciplinare di Matematica, Vol. 8 (2009), pp. 1- 41.

 

2010

 

[73] (con S. Milella) Degenerate differential equations and modified Szász-Mirakjan operators, Rend. Circ. Mat. Palermo, 59 (2010), 227-250, DOI: 10.1007/s12215-010-0017-z

 

[74] (con M. Cappelletti Montano e V. Leonessa) On a generalization of Kantorovich operators on simplices and hypercubes, Adv. Pure Appl. Math. 1 (2010), 359 – 385.

 

[75] (con G. Musceo) Degenerate second-order differential operators with generalized reflecting barriers boundary conditions, to appear in Math. Reports, Vol. 12 (62) (2010), no. 2.

 

[76] (with S. Diomede) Asymptotic formulae for positive linear operators: direct and converse results, Jaén J. Approx., 2(2) (2010), 255 - 287.

 

2011

 

[77] (con M. Cappelletti Montano e S. Diomede) Degenerate elliptic operators, Feller semigroups and modified Bernstein-Schnabl operators, Math. Nachr. 284, No. 5–6, 587 – 607 (2011) / DOI 10.1002/mana.200810196

 

[78] (con M. Cappelletti Montano e V. Leonessa) Iterates of multidimensional Kantorovich-type operators and their associated positive C0-semigroups, Studia Univ. Babeş-Bolyai Math. 56(2011), no. 2, 219 – 235.

 

 

[79] (with S. Milella and G. Musceo) On a class of positive C0-semigroups on weighted continuous function spaces, Note Mat. 31 (2011), no. 1, 15-27.

 

[80] (with S. Milella and G. Musceo) Multiplicative perturbations of the Laplacian and related approximation problems, J. Evol. Equ. 11(2011), 771 - 792, DOI: 10.1007/s00028-011-0110-6,

 

 

2012

 

[81] (with I. Raşa) Lipschitz contractions, unique ergodicity and asymptotics of Markov semigroups, Bollettino U.M.I. (9) V (2012), 1 - 17.

 

 

[82] (with M. Cappelletti Montano e V. Leonessa) On a generalization of Szász-Mirakjan-Kantorovich operators, to appear in Results Math., 2012, DOI: 10.1007/s00025-012-0236-z

2013

 

 

[83] On some convergence criteria for nets of positive operators on continuous function spaces, J. Math. Anal. Appl. 398 (2013) 542 - 552, DOI 10.1016/j.jmaa.2012.09.010.

 

Preprints

 

 

Other articles

 

1997

 

[1] Korovkin - type theorem, in “Encyclopaedia of Mathematics”, Kluwer Academic Publishers, Dordrecht, 1997.

 

[2] Korovkin - type approximation theory, in “Encyclopaedia of Mathematics”, Kluwer Academic Publishers, Dordrecht, 1997.

 

2000

 

[3] Bauer simplex, in “Encyclopaedia of Mathematics”, Kluwer Academic Publishers, Dordrecht, 2000.

 

 

 

Editorial activities

 

Mathematical Journals

 

· Mediterranean Journal of Mathematics, published by Birkhäuser Verlag, Basel,

 

Published volumes:

 

Vol. 1, 2004, 4 issues, pp. 1-499;

Vol. 2, 2005, 4 issues, pp. 1-481;

Vol. 3, 2006, 4 issues, pp. 1-592;

Vol. 4, 2007, 4 issues, pp. 1-503;

Vol. 5, 2008, 4 issues, pp. 1- 500;

Vol. 6, 2009, 4 issues, pp. 1- 508;

Vol. 7, 2010, 4 issues, pp. 1- 603;

Vol. 8, 2011, 4 issues, pp. 1- 636;

Vol. 9, 2012, 4 issues, pp. 1-926;

 

Proceedings

 

[1] F.Altomare et al. Eds, Trends in Functional Analysis and Approximation Theory, Proceedings of the Conference  held in Acquafredda di Maratea, September 10-15,  1989,  Atti  del  Seminario Matematico  e  Fisico  dell'Università di  Modena, Monograf, Bologna 1991. MR 92f: 00028.

 

[2] F.Altomare and G.Mastroianni Eds., Functional  Analysis and Approximation  Theory   II,   Proceedings   of   the   Second  International   Conference   on   Functional   Analysis   and  Approximation Theory held  in Acquafredda  di Maratea (Potenza), September 14-19, 1992,  Rend.  Circ.  Mat.  Palermo, Serie II, Suppl. 33, 1993, Voll. I and II.

 

[3] F.Altomare et al. Eds., Functional Analysis and Approximation Theory III, Proceedings of the 3rd  International  Conference on Functional  Analysis  and  Approximation  Theory  held  in Acquafredda di Maratea (Potenza), September 23  -  28,  1996,  Suppl. Rend. Circ. Mat. Palermo, n. 52 (1998), Voll. I and II.

 

[4] F.Altomare et al. Eds., Functional Analysis and Approximation Theory IV, Proceedings of the 4th  International  Conference on Functional  Analysis  and  Approximation  Theory  held  in Acquafredda di Maratea (Potenza), September 22  -  28,  2000,  Rend. Circ. Mat. Palermo, Serie II, Suppl. 68(2002), Voll. I and II.

 

[5] F. Altomare et al. Eds., Operator Methods for Evolution Equations and Approximation Problems, Proceedings of the International Summer School on Operator Methods for Evolution Equations and Approximation Problems, Monopoli – Italy, September 15-22, 2002, Aracne Editrice, Roma, 2003.

 

[6] F.Altomare et al. Eds., Functional Analysis and Approximation Theory V, Proceedings of the 5th  International  Conference on Functional  Analysis  and  Approximation  Theory  held  in Acquafredda di Maratea (Potenza), June 16 – 23,   2004,  Rend. Circ. Mat. Palermo, Serie II, Suppl. 76(2005), pp. 1 – 700.

 

[7] International Mediterranean Congress of Mathematics Almeria 2005, Almeria, Spain, June 6-10, 2005, Mediterr. J. of Math., Vol. 3(2006), no2, pp. 119 – 345.

 

[8] A special Issue dedicated to the memory of Professor Aldo Cossu (1922 – 2005), Mediterr. J. of Math., Vol. 3(2006), no. 3-4, pp.347 – 592.

 

[9] F. Altomare, 18th Congress of Unione Matematica Italiana (Bari, September 24 – 29, 2007), UMIProceedings Vol. 3, pp. 1 – 518, Unione Matematica Italiana, Bologna, 2008.

 

[10] F.Altomare et al. Eds., Functional Analysis and Approximation Theory VI, Proceedings of the 6th  International  Conference on Functional  Analysis  and  Approximation  Theory  held  in Acquafredda di Maratea (Potenza), September 24 – 30,   2009,  Rend. Circ. Mat. Palermo, Serie II, Suppl. 82(2010), pp. 1 – 460.

 

 
  Ultima modifica: 10/01/2013