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Ricerca

I miei interessi di ricerca riguardano principalmente l'Analisi Funzionale, l'Analisi Reale e la Teoria dell'Approssimazione e sono in particolare orientati allo studio delle proprietà di approssimazione di varie famiglie di operatori, integrali e discreti, tra cui le serie sampling generalizzate e gli operatori sampling-Kantorovich, che hanno importanti connessioni con problemi di ricostruzione di segnali ed immagini, in diversi spazi di funzioni, con particolare attenzione agli spazi di funzioni a variazione limitata.

Mi research interests are mainly about Functional Analysis, Real Analysis and Approximation Theory. In particular I am interested in the approximation properties of several families of integral and discrete operators, among them the generalized sampling series and the sampling-Kantorovich operators, that have important connections with some problems of Signal and Image Processing, in different function spaces, with particular attention to the spaces of functions with bounded variation.

Pubblicazioni - Papers

  1. L. Angeloni, G. Vinti, A unified approach to approximation results with applications to nonlinear sampling theory, Int. J. Math. Sciences, 3(1) (2004), 93--128.
  2. L. Angeloni, A. Martellotti, A separation theorem with applications to Edgeworth equivalence in some infinite dimensional setting, Comment. Math. Prace Mat., 44(2) (2004), 227--243.
  3. L. Angeloni, G. Vinti, Rate of approximation for nonlinear integral operators with application to signal processing, Differential Integral Equations, 18(8) (2005), 855--890.
  4. L. Angeloni, Metodi di separazione in economia matematica: uguaglianza di Edgeworth, arbitraggio ed informazione asimmetrica, estratto dalla tesi di dottorato dal titolo Separation methods in mathematical economics: Edgeworth Equivalence, arbitrage and asymmetric information, fascicolo speciale del Bollettino UMI dedicato alle tesi di dottorato discusse nell'anno 2004 (2005).
  5. L. Angeloni, B. Cornet, Existence of Financial Equilibria in a Multiperiod Stochastic Economy, Advances in Mathematical Economics, 8 (2006), 1--31.
  6. L. Angeloni, G. Vinti, Convergence in Variation and Rate of Approximation for Nonlinear Integral Operators of Convolution Type, Results Math., 49 (2006), 1--23; DOI: 10.1007/s00025-006-0208-2. Erratum: 57 (2010), 387--391.
  7. L. Angeloni, A. Martellotti, Non-coalitional Core-Walras equivalence in finitely additive economies with extremely desirable commodities, Mediterranean Journal of Mathematics, 4(1) (2007), 87--107.
  8. L. Angeloni, G. Vinti, Approximation by means of nonlinear integral operators in the space of functions with bounded \phi-variation, Differential Integral Equations, 20(3) (2007), 339--360. Erratum: 23(7-8) (2010), 795--799.
  9. L. Angeloni, V.F. Martins-da-Rocha, Large economies with differential information and free disposal, Economic Theory, 38(2) (2009), 263--286, DOI: 10.1007/s00199-008-0369-1
  10. L. Angeloni, G. Vinti, Convergence and rate of approximation for linear integral operators in BV^{\phi}-spaces in multidimensional setting, Journal of Mathematical Analysis and Applications, 349(2) (2009), 317--334, DOI:10.1016/j.jmaa.2008.08.029. 
  11. L. Angeloni, G. Vinti, Approximation with respect to Goffman-Serrin variation by means of non-convolution type integral operators, Numerical Functional Analysis and Optimization, 31 (2010), 519--548, DOI: 10.1080/01630563.2010.490549
  12. L. Angeloni, A characterization of a modulus of smoothness in multidimensional setting, Bollettino dell’Unione Matematica Italiana, Serie IX, 4 (1) (2011), 79--108.
  13. L. Angeloni, Convergence in variation for a homothetic modulus of smoothness in multidimensional setting, Communications on Applied Nonlinear Analysis, 19(1) (2012), 1--22.
  14. L. Angeloni, Approximation results with respect to multidimensional \phi-variation for nonlinear integral operators, Z. Anal. Anwendungen 32(1)(2013), 103-128.
  15. L. Angeloni, G. Vinti, A sufficient condition for the convergence of a certain modulus of smoothness in multidimensional setting, Communications on Applied Nonlinear Analysis, 20(1) (2013), 1--20.
  16. L. Angeloni, G. Vinti, Approximation in variation by homothetic operators in multidimensional setting, Differential Integral Equation, 26(5-6) (2013), 655--674.
  17. L. Angeloni, G. Vinti, Variation and approximation for Mellin-type operators, In: Proceeding of SampTA2013. 10th International Conference on Sampling Theory and Applications, EURASIP, 2013, 178--181.
  18. L. Angeloni, G. Vinti, Variation and approximation in multidimensional setting for Mellin integral operators, New Perspectives on Approximation and Sampling Theory-Festschrift in honor of Paul Butzer’s 85th birthday, Birkhauser, (2014) 299--317.
  19. L. Angeloni, G. Vinti, Convergence and rate of approximation in BV^{\phi}(R^N_+) for a class of Mellin integral operators, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 25 (2014), 217--232.
  20. L. Angeloni, G. Vinti, Approximation in variation for nonlinear Mellin integral operators in multidimensional setting, In: Recent Advances in Applied Mathematics, Modelling and Simulation, Proceedings of the 8th International Conference on Applied Mathematics, Simulation and Modelling (ASM '14), WSEAS Press, 2014, 199--203.
  21. L. Angeloni, G. Vinti, Approximation in variation for Mellin integral operators, PAMM (Proceedings in Applied Mathematics and Mechanics), 15 (2015), 649--650.
  22. L. Angeloni, G. Vinti, A characterization of absolute continuity by means of Mellin integral operators, Z. Anal. Anwendungen, 34(3) (2015), 343--356.
  23. L. Angeloni, G. Vinti, Convergence in variation and a characterization of the absolute continuity, Integral Transforms Spec. Funct., 26(10) (2015),829--844.
  24.  L. Angeloni, G. Vinti, A concept of absolute continuity and its characterization in terms of convergence in variation, Mathematische Nachrichten, 289(16) (2016), 1986--1994. DOI: 10.1002/mana.201500271.
  25. L. Angeloni, G. Vinti, A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation, J. Function Spaces, Article ID 3843921, 2016. DOI: http://dx.doi.org/10.1155/2016/3843921. 
  26. L. Angeloni, A new concept of multidimensional variation in the sense of Riesz and applications to integral operators, Mediterranean Journal of Mathematics, 14(4) (2017), 149. DOI: http://dx.doi.org/10.1007/s00009-017-0947-1.
  27. L. Angeloni, G. Vinti, Discrete operators of sampling-type and approximation in phi-variation, Mathematische Nachrichten, 291 (2018), 546--555. DOI: http://dx.doi.org/10.1002/mana.201600508.
  28. L. Angeloni, D. Costarelli, G. Vinti, A characterization of the convergence in variation for the generalized sampling series, Ann. Acad. Sci. Fenn. Math., 43 (2018), 755--767.
  29. L. Angeloni, D. Costarelli, G. Vinti, A characterization of the absolute continuity in terms of convergence in variation for the sampling Kantorovich operators, Med. J. Math., 16: 44 (2019). 
  30. L. Angeloni, D. Costarelli, G. Vinti, Quantitative estimates for sampling type operators with respect to the Jordan variation, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 31(2) (2020), 269--284.
  31. L. Angeloni, D. Costarelli, G. Vinti, Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing, Ann. Acad. Sci. Fenn. Math., 45 (2020), 75--770.
  32. L. Angeloni, E. Liflyand, G. Vinti, Tonelli variation, real Hardy spaces, and integrability of the Fourier transform, Complex Analysis and Operator Theory,  14(6), article n.64, (2020).
  33. L. Angeloni, J. Appell, S. Reinwand, Some Remarks on Vainikko Integral Operators in BV Type Spaces, Boll. Unione Mat. Ital., Special Issue "Measure, Integration and Applications" dedicated to Prof. Domenico Candeloro, (2020) 555--565.
  34. L. Angeloni, D. Costarelli, M. Seracini, G. Vinti, L. Zampogni, Variation diminishing-type properties for multivariate sampling Kantorovich operators, Boll. Unione Mat. Ital., Special Issue "Measure, Integration and Applications" dedicated to Prof. Domenico Candeloro, 13 (2020), 595--605. DOI: https://doi.org/10.1007/s40574-020-00256-3.
  35. L. Angeloni, D. Costarelli, G. Vinti, Approximation properties of mixed sampling-Kantorovich operators, R. Acad. Cienc. Exactas Fis. Nat. Serie A. Matemáticas, 115 article n. 4 (2021). DOI: 10.1007/s13398-020-00936-x.
  36. L. Angeloni, N. Cetin, D. Costarelli, A.R. Sambucini, G. Vinti, Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces, Constructive Mathematical Analysis, 4(2) (2021), 229--241. 
  37. L. Angeloni, C. Conti, S. De Marchi, E. Francomano, G. Vinti, Multivariate approximation: Theory and applications 2020, Dolomites Research Notes on Approximation, 14(2) (2021), I-II.
  38. L. Angeloni, G. Vinti, Estimates in variation for multivariate sampling-type operators, Dolomites Research Notes on Approximation, 14(2) (2021), 1--9.
  39. L. Angeloni, J. Appell, T. D. Benavides, S. Reinwand, G. Vinti, Compactness properties of multiplication and substitution operators, J. Operator Theory, 89(1) (2023), 23--48.
  40. L. Angeloni, N. Merentes, M.A. Valera López, Convolution Integral Operators in Variable Bounded Variation Spaces, Mediterr. J. Math., 20:141 (2023). DOI: https://doi.org/10.1007/s00009- 023-02358-6.
  41. L. Angeloni, G. Vinti, Multidimensional sampling-Kantorovich operators in BV-spaces, Open Mathematics, 21(1) (2023), pp. 20220573.

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