A general approximation result for nonlinear integral operators and applications to signal processing

Applicable Analysis

Volumn 79, Issue 1-2, 2001, Pages 217-238

  Vinti, Gianluca ^a  

^a UNIVERSITY OF PERUGIA   (Italy)

Author keywords

Generalized sampling series; Jensen's inequality; Modular convergence; Orlicz space; Topological groups

Indexed keywords

EID: 27844511616     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036810108840958     Document Type: Article

References (42)

1. Barbieri, F., 1983. Approssimazione mediante nuclei momento. Atti. Sem. Mat. Fis. Univ. Modena, 32: 308–328.
2. Bardaro, C., 1984. On approximation properties for some classes of linear operators of convolution type. Atti. Sem. Mat. Fis. Univ. Modena, 33: 329–356.
3. Bardaro, C., and Mantellini, I., 1998. Modular approximation by sequences of nonlinear integral operators in Musielak-Orlicz spaces. Atti. Sem. Mat. Fis. Univ. Modena. Suppl, 46: 403–425. A special issue of the International Conference in Honour of Prof. Calogero Vinti
4. Bardaro, C., and Mantellini, I., 2000. “ Linear integral operators with homogeneous kernel: approximatioin properties in modular spaces. Applications to Mellintype convolution operators and to some classes of fractional integrals ”. In Applied Math. Rev Edited by: Anastassiou, G., Vol. 1, 45–67. Singapore
5. Bardaro, C., Musielak, J., and Vinti, G., 1994. Modular estimates and modular convergence for a class of nonlinear opeerators. Mathematica Japonica, 39: 7–14.
6. Bardaro, C., Musielak, J., and Vinti, G., 1996. Approximation by nonlinear integral operators in some modular function spaces. Annales Polonici Math, 53: 173–182.
7. Bardaro, C., Musielak, J., and Vinti, G., 1997. Nonlinear opeartors of integral type in some functional spaces. Collectanea Math, 48: 409–422.
8. Bardaro, C., and Vinti, G., 1989. Modular convergence in generalized Orlicz spaces for moment type operators. Applicable Analysis, 32: 265–276.
9. Bardaro, C., and Vinti, G., 1994. Genearl convergence theorem with respect to Cesari variation and applications. Nonlinear Analysis Theory and Appl, 22: 505–518.
10. Bardaro, C., and Vinti, G., 1997. A general approach to the convergence theorems of generalized sampling series. Applicable Analysis, 64: 203–217.
11. Bardaro, C., 1998. Uniform convergence and rate of approximation for a nonlinear version of the generalized sampling operator. Result. Math, 34: 224–240.
12. Bezuglaya, L., and Katsnelson, V., 1993. The sampling theorem for functions with limited multi-band spectrum I. Zeitschrif für Analysis und ihre Anwendungen, 12: 511–534.
13. Butzer, P.L., 1983. A survey of the Whittaker-Shannon sampling theorem and some of its extensions. J. Math. Res. Exposition, 3: 185–212.
14. Butzer, P.L., Fisher, A., and Stens, R.L., 1990. Generalized sampling approximation of multivariate signals: theory and applications. Note di Matematica, 10 (1): 173–191.
15. Butzer, P.L., and Hinsen, G., 1989. Reconstruction of bounded signal from peudo-periodic, irregularly spaced samples. Signal Processing, 17: 1–17.
16. Butzer, P.L., and Jansche, S., 1997. A direct approach to the Mellin Transform. J. Fourier Anal. Appl, 3: 325–376.
17. Butzer, P.L., and Jansche, S., 1998. The exponential sampling theorem of signal analysis. Atti. sem. Mat. Fis. Univ. Modena, 46: 99–122. a special volume dedicated to Professor Calogero Vinti
18. Butzer, P.L., and Nessel, R.J., 1971. “ Fourier Analysis and Approximation I ”. London: Academic Press.
19. Butzer, P.L., and Stens, R.L., 1993. “ Linear prediction by samples from the past ”. In Advanced Topics in Shannon Sampling and Interpolation Theory Edited by: Marks II, R.J., Springer-Verlag, New York
20. Degani Cattelani, F., 1981. Nuclei di tipo distanza che attutiscono i salti in una o piú variabili. Atti. Sem. Mat. Fis. Univ. Modena, 30: 299–321.
21. Dodson, M.M., and Silva, A.M., 1985. Fourier analysis and the Sampling Theorem. Proc. Ir. Acad, 86A: 81–108.
22. Folland, G.B., 1984. “ Real Analysis:Modern techniques and their applications ”. New York: Wiley & Sons.
23. Gogatishvili, A., and Kikilashvili, V., 1993. Crieria of weighted inequalities in Orlicz classed for maximal functions defined on homogeneous type spaces. Proc. Georgian Acad. Sci. Math, 6: 617–645.
24. Haber, S., and Shisha, O., 1974. Improper integrals, simple integrals, and numerical quadrature. Journal of Approximation Theory, 11: 1–15.
25. Higgins, J.R., 1996. “ Sampling Theory in Fourier and Signal Analysis: Foundations ”. Oxford: Oxford University Press.
26. Higgins, J.R., and Stens, R.L., 1999. “ Sampling Theory in Fourier and Signal Analysis ”. In Advanced Topics, Oxford University Press. Oxford Science Publications
27. Kozlowski, W.M., “ Modular Function Spaces ”. In Pure Appl. Math, Marcel Dekker.
28. Krasnosel'skiǐ, M.A., and Rutickiǐ, Ya.B. 1961. Convex functions and Orlicz spaces. P.Noordhoff Ltd..
29. Maligranda L., Orlicz Spaces and Interpolation. Seminarios de Matematica 1989 IMECC, Campinas
30. Mantellini, I., and Vinti, G., 1996. Modular estimates for nonlinear integral operators and applications in fractional calculus. Numer. Funct. Anal. and Optimiz, 17 (1&2): 143–165.
31. Mantellini, I., and Vinti, G., 1998. ф-Variation and Nonlinear Integral Operators. Atti. Sem. Mat. Fis. Univ. Modena, 46: 847–862. a special issue of the International Conference in Honour of Prof. Calogero Vinti
32. Musielak, J., 1983. Orlicz Spaces and Modular Spaces. Lecture Notes in Math, 1034
33. Musielak, J., 1994. On the approximation by nonlinear integral operators with generalized Lipschitz kernel over a locally compact a belian group. Commentationes Math, 34: 153–164.
34. Musielak, J., and Orlicz, W., 1959. On modular spaces. Studia Math, 28: 49–65.
35. Rao, M.M., and Ren, Z.D., 1991. “ Theory of Orlicz spaces ”. In Pure and Appl. Math, Basel, Hong Kong: Marcel Dekker Inc.
36. Ries, S., and Stens, R.L., 1984. Approximation by generalized sampling series. Constructive Theory of Functions, 84: 746–756.
37. Vinti, C., 1959. Sopra una classe di funzionali che approssimano l'area di una superficie. Annali di Mat. Pura e Appl, 48 (4): 237–255.
38. Vinti, c., 1964. Perimetro — Variazione. Annali Scuola Norm. Sup. Pisa, 43 (4): 201–231.
39. Vinti, C., 1964. Sull'approssimazione in perimetro e in area. Atti. Sem. Mat. Fis. Univ. Modena, 13: 187–197.
40. Vinti, C., 1998. A Survey on Recent Results of the Mathematical Seminar in Perugia. inspired by the Work of Professor P.L. Butzer. Result. Math, 34: 32–55.
41. Vinti, G., 1994. Generalized ф-variation in the sense of Vitali: estimates for integral operators and applications in fractional calculus. Commentationes Math, 34: 199–213.
42. Zanelli, V., 1981. Funzioni momento convergenti dal basso in variazione di ordine non intero. Atti. Sem. Mat. Fis. Univ. Modena, 30: 355–369.