Order of approximation for sampling Kantorovich operators

Journal of Integral Equations and Applications

Volumn 26, Issue 3, 2014, Pages 345-368

  Costarelli, Danilo ^a   Vinti, Gianluca ^b  

^a ROMA TRE UNIVERSITY   (Italy)

^b UNIVERSITY OF PERUGIA   (Italy)

Author keywords

Irregular sampling; Lipschitz classes; Order of approximation; Orlicz spaces; Sampling Kantorovich operators

Indexed keywords

EID: 84903447886     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/JIE-2014-26-3-345     Document Type: Article

References (40)

1. L. Angeloni and G. Vinti, Rate of approximation for nonlinear integral operators with applications to signal processing, Diff. Integ. Equat. 18 (2005), 855-890.
2. J. Appell, The importance of being Orlicz, in Orlicz centenary volume, Banach Center Publ., Polish Acad. Sci. 64, 2004.
3. C. Bardaro, P.L. Butzer, R.L. Stens and G. Vinti, Approximation of the Whittaker Sampling Series in terms of an average modulus of smoothness covering discontinuous signals, J. Math. Anal. Appl. 316 (2006), 269-306.
4. C. Bardaro, Kantorovich-type generalized sampling series in the setting of Orlicz spaces, Sampl. Theor. Signal Image Process. 6 (2007), 29-52.
5. C. Bardaro, Prediction by samples from the past with error estimates covering discontinuous signals, IEEE Trans. Infor. Theor. 56 (2010), 614-633.
6. C. Bardaro and I. Mantellini, Modular approximation by sequences of nonlin- ear integral operators in Musielak-Orlicz Spaces, Att. Mat. Fis. Univ. Modena 46 (1998), 403-425.
7. C. Bardaro and I. Mantellini, On convergence properties for a class of Kantorovich discrete oper- ators, Numer. Funct. Anal. Optim. 33 (2012), 374-396.
8. C. Bardaro, J. Musielak and G. Vinti, Nonlinear integral operators and applications, De Gruyter Ser. Nonlin. Anal. Appl. 9, 2003.
9. C. Bardaro and G. Vinti, Some inclusion theorems for Orlicz and Musielak-Orlicz type spaces, Ann. Mat. Pura Appl. 168 (1995), 189-203.
10. C. Bardaro and G. Vinti, A general approach to the convergence theorems of generalized sampling series, Appl. Anal. 64 (1997), 203-217.
11. C. Bardaro and G. Vinti, Uniform convergence and rate of approximation for a nonlinear version of the generalized sampling operator, Results Math. 34 (1998), 224-240.
12. C. Bardaro and G. Vinti, An abstract approach to sampling type operators inspired by the work of P.L. Butzer-Part I-Linear operators, Samp. Theor. Signal Image Proc. 2 (2003), 271-296.
13. L. Bezuglaya and V. Katsnelson, The sampling theorem for functions with limited multi-band spectrum I, Z. Anal. Anwend. 12 (1993), 511-534.
14. P.L. Butzer and R.J. Nessel, Fourier analysis and approximation I, Aca- demic Press, New York, 1971.
15. P.L. Butzer, S. Ries and R.L. Stens, Approximation of continuous and discontinuous functions by generalized sampling series, J. Approx. Theor. 50 (1987), 25-39.
16. P.L. Butzer and R.L. Stens, Sampling theory for not necessarily band-limited functions: A historical overview, SIAM Rev. 34 (1992), 40-53.
17. P.L. Butzer and R.L. Stens, Linear prediction by samples from the past, in Advanced topics in Shannon sampling and interpolation theory, R.J. Marks, II, ed., Springer-Verlag, New York, 1993.
18. F. Cluni, D. Costarelli, A.M. Minotti and G. Vinti, Multivariate sampling Kantorovich operators: Approximation and applications to civil engineering, in EURASIP, Proc. SampTA 2013, 10th Int. Conf. Sampl. Theor. Appl., 400-403.
19. D. Costarelli and G. Vinti, Approximation by multivariate generalized sam- pling Kantorovich operators in the setting of Orlicz spaces, Boll. U.M.I. 4 (2011), 445-468.
20. D. Costarelli and G. Vinti, Approximation by nonlinear multivariate sampling Kantorovich type operators and applications to image processing, Num. Funct. Anal. Optim. 34 (2013), 819-844.
21. M.M. Dodson and A.M. Silva, Fourier analysis and the sampling theorem, Proc. Irish Acad. 86 (1985), 81-108.
22. C. Donnini and G. Vinti, Approximation by means of Kantorovich gener- alized sampling operators in Musielak-Orlicz spaces, PanAmer. Math. J. 18 (2008), 1-18.
23. J.R. Higgins, Five short stories about the cardinal series, Bull. Amer. Math. Soc. 12 (1985), 45-89.
24. J.R. Higgins, Sampling theory in Fourier and signal analysis: Foundations, Oxford University Press, Oxford, 1996.
25. J.R. Higgins and R.L. Stens, Sampling theory in Fourier and signal analysis:Advanced topics, Oxford Science Publications, Oxford University Press, Oxford, 1999.
26. A.J. Jerry, The Shannon sampling-Its various extensions and applications:A tutorial review, Proc. IEEE 65 (1977), 1565-1596.
27. W.M. Kozlowski, Modular function spaces, Pure Appl. Math. Marcel Dekker, New York, 1988.
28. M.A. Krasnosel'skiĂ and Ya.B. RutickiĂ, Convex functions and Orlicz spaces, P. Noordhoff Ltd., Groningen, The Netherlands, 1961.
29. L. Maligranda, Orlicz spaces and interpolation, Sem. Mat. IMECC, Camp- inas, 1989.
30. J. Musielak, Orlicz spaces and modular spaces, Lec. Notes in Math. 1034, Springer-Verlag, New York, 1983
31. J. Musielak and W. Orlicz, On modular spaces, Stud. Math. 28 (1959), 49-65.
32. M.M. Rao and Z.D. Ren, Theory of Orlicz spaces, Pure Appl. Math., Marcel Dekker, Inc., New York, 1991.
33. M.M. Rao and Z.D. Ren, Applications of Orlicz spaces, Mono. Text. Pure Appl. Math. 250, Marcel Dekker, Inc., New York, 2002.
34. S. Ries and R.L. Stens, Approximation by generalized sampling series, in Constructive theory of functions'84, Sofia, 1984.
35. C.E. Shannon, Communication in the presence of noise, Proc. I.R.E. 37 (1949), 10-21.
36. C. Vinti, A survey on recent results of the mathematical seminar in Perugia, inspired by the work of Professor P.L. Butzer, Result. Math. 34 (1998), 32-55.
37. G. Vinti, A general approximation result for nonlinear integral operators and applications to signal processing, Appl. Anal. 79 (2001), 217-238.
38. G. Vinti, Approximation in Orlicz spaces for linear integral operators and applications, Rend. Circ. Mat. Palermo 76 (2005), 103-127.
39. G. Vinti and L. Zampogni, Approximation by means of nonlinear Kan- torovich sampling type operators in Orlicz spaces, J. Approx. Theor. 161 (2009), 511-528.
40. G. Vinti and L. Zampogni, A unifying approach to convergence of linear sampling type opera- tors in Orlicz spaces, Adv. Differ. Equat. 16 (2011), 573-600.