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Applicable Analysis
An International Journal
Volume 79, 2001 - Issue 1-2
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Original Articles

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

Pages 217-238 | Published online: 02 May 2007

References

  • Barbieri , F. 1983 . Approssimazione mediante nuclei momento . Atti. Sem. Mat. Fis. Univ. Modena , 32 : 308 – 328 .
  • Bardaro , C. 1984 . On approximation properties for some classes of linear operators of convolution type . Atti. Sem. Mat. Fis. Univ. Modena , 33 : 329 – 356 .
  • 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
  • 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
  • Bardaro , C. , Musielak , J. and Vinti , G. 1994 . Modular estimates and modular convergence for a class of nonlinear opeerators . Mathematica Japonica , 39 : 7 – 14 .
  • Bardaro , C. , Musielak , J. and Vinti , G. 1996 . Approximation by nonlinear integral operators in some modular function spaces . Annales Polonici Math , 53 : 173 – 182 .
  • Bardaro , C. , Musielak , J. and Vinti , G. 1997 . Nonlinear opeartors of integral type in some functional spaces . Collectanea Math , 48 : 409 – 422 .
  • Bardaro , C. and Vinti , G. 1989 . Modular convergence in generalized Orlicz spaces for moment type operators . Applicable Analysis , 32 : 265 – 276 .
  • Bardaro , C. and Vinti , G. 1994 . Genearl convergence theorem with respect to Cesari variation and applications . Nonlinear Analysis Theory and Appl , 22 : 505 – 518 .
  • Bardaro , C. and Vinti , G. 1997 . A general approach to the convergence theorems of generalized sampling series . Applicable Analysis , 64 : 203 – 217 .
  • Bardaro , C. 1998 . Uniform convergence and rate of approximation for a nonlinear version of the generalized sampling operator . Result. Math , 34 : 224 – 240 .
  • 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 .
  • Butzer , P.L. 1983 . A survey of the Whittaker-Shannon sampling theorem and some of its extensions . J. Math. Res. Exposition , 3 : 185 – 212 .
  • 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 .
  • Butzer , P.L. and Hinsen , G. 1989 . Reconstruction of bounded signal from peudo-periodic, irregularly spaced samples . Signal Processing , 17 : 1 – 17 .
  • Butzer , P.L. and Jansche , S. 1997 . A direct approach to the Mellin Transform . J. Fourier Anal. Appl , 3 : 325 – 376 .
  • 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
  • Butzer , P.L. and Nessel , R.J. 1971 . “ Fourier Analysis and Approximation I ” . London : Academic Press .
  • 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
  • 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 .
  • Dodson , M.M. and Silva , A.M. 1985 . Fourier analysis and the Sampling Theorem . Proc. Ir. Acad , 86A : 81 – 108 .
  • Folland , G.B. 1984 . “ Real Analysis:Modern techniques and their applications ” . New York : Wiley & Sons .
  • 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 .
  • Haber , S. and Shisha , O. 1974 . Improper integrals, simple integrals, and numerical quadrature . Journal of Approximation Theory , 11 : 1 – 15 .
  • Higgins , J.R. 1996 . “ Sampling Theory in Fourier and Signal Analysis: Foundations ” . Oxford : Oxford University Press .
  • Higgins , J.R. and Stens , R.L. 1999 . “ Sampling Theory in Fourier and Signal Analysis ” . In Advanced Topics , Oxford University Press . Oxford Science Publications
  • Kozlowski , W.M. “ Modular Function Spaces ” . In Pure Appl. Math , Marcel Dekker .
  • Krasnosel'skiǐ , M.A. and Rutickiǐ , Ya.B . 1961 . Convex functions and Orlicz spaces . P.Noordhoff Ltd. ,
  • Maligranda L. Orlicz Spaces and Interpolation. Seminarios de Matematica 1989 IMECC, Campinas
  • 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 .
  • 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
  • Musielak , J. 1983 . Orlicz Spaces and Modular Spaces . Lecture Notes in Math , 1034
  • 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 .
  • Musielak , J. and Orlicz , W. 1959 . On modular spaces . Studia Math , 28 : 49 – 65 .
  • Rao , M.M. and Ren , Z.D. 1991 . “ Theory of Orlicz spaces ” . In Pure and Appl. Math , Basel, , Hong Kong : Marcel Dekker Inc .
  • Ries , S. and Stens , R.L. 1984 . Approximation by generalized sampling series . Constructive Theory of Functions , 84 : 746 – 756 .
  • 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 .
  • Vinti , c. 1964 . Perimetro — Variazione . Annali Scuola Norm. Sup. Pisa , 43 ( 4 ) : 201 – 231 .
  • Vinti , C. 1964 . Sull'approssimazione in perimetro e in area . Atti. Sem. Mat. Fis. Univ. Modena , 13 : 187 – 197 .
  • 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 .
  • 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 .
  • Zanelli , V. 1981 . Funzioni momento convergenti dal basso in variazione di ordine non intero . Atti. Sem. Mat. Fis. Univ. Modena , 30 : 355 – 369 .

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