Publication Cover
Applicable Analysis
An International Journal
Volume 64, 1997 - Issue 3-4
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Original Articles

A general approach to the convergence theorems of generalized sampling series

Pages 203-217 | Received 01 Nov 1996, Published online: 02 May 2007

  • 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 Vinti , G. 1989 . Modular convergence in generalized Orlicz spaces for moment type operators . Applicable Analysis , 32 : 265 – 276 .
  • Bardaro , C. and Vinti , G. 1995 . Modular estimates for linear integral operators in Musielak-Orliez spaces on groups . Atti Sem. Mat. Fis. Univ. Modena , 43 : 483 – 490 .
  • Bardaro , C. and Vinti , G. 1995 . Modular estimates and modular convergence for linear integral operators . Contemporary Math. , 190 : 95 – 105 .
  • Bardaro C. Mantellini I. A modular convergence theorem for general nonlinear integral operators to appear in Commentations Matematicae.
  • Bardaro C. Mantellini I. Modular approximation by sequences of nonlinear integral opearators in Musielak-Orlicz spaces to appear in Atti Sem. Mat. Fis. Univ. Modena.
  • Butzer P.L. Jansche S. Mellin Transforms, the Mellin-Poisson Summation Formula and the Exponential Sampling Theorem to appear.
  • Butzer , P.L. and Nessel , R.J. 1971 . Fourier Analysis and Approximation , Academic Press .
  • Butzer , P.L. and Stens , R.L. 1983 . The Euler-Maclaurin summation formula, the sampling theorems, and the approximate integration over the real axis . Linear Algebra and its Applications , 52-53 : 141 – 155 .
  • 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. New York : Springer-Verlag .
  • Butzer , P.L. and Stens , R.L. 1992 . Sampling theory for not necessarily bandlimited functions: a historical overview . SIAM Review , 34 : 40 – 53 .
  • Butzer , P.L. , Fisher , A. and Stens , R.L. 1990 . Generalized sampling approximation of multivariate signals: theory and application . Note di Matematica , 10 : 173 – 191 . Suppl. n.1
  • Butzer P.L. Gessinger A. The approximate sampling theorem, Poisson's sum formula, a decomposition theorem for Parseval's equation and their interconnections. to appear.
  • Degani Cattelani , F. 1981 . Nuclei di tipo “distanza” che attutiscono i salti in una o piú dimensioni . Atti Sem. Mat. Fis. Univ. Modena , 30 : 299 – 321 .
  • Folland , G.B. 1984 . Real Analysis: Modern techniques and their applications , Wiley and sons .
  • Haber , S. and Shisha , O. 1974 . Improper integrals, simple integrals, and numerical quadrature . Journal of Approximation Theory , 11 : 1 – 15 .
  • Hewitt , E. and Ross , K.A. 1963 . Abstract Harmonic Analysis , Berlin : Springer-Verlag . Göttingen
  • Higgins , J.R. 1996 . Sampling Theory in Fourier and Signal Analysis: Foundations , Oxford : Oxford Univ. Press .
  • Hidelbrandt , T.H. 1963 . “ Introduction to the Theory of Integration ” . In Pure Appl. Math. , New York : Academic Press . London
  • Kozlowski , W.M. 1988 . “ Modular Function Spaces ” . In Pure Appl. Math. , New York : Marcel Dekker . Basel
  • Musielak , J. 1983 . “ Orlicz Spaces and Modular Spaces ” . In Lecture Notes in Math. , Vol. 1034 , Springer-Verlag .
  • Musielak , J. . Functional Analysis and Applications . Proceedings Confer. . Oberwolfach. Vol. 1980 , pp. 99 – 110 . Birkhäuser-Verlag .
  • Musielak , J. 1994 . On the approximation by nonlinear integral operators with generalized Lipschitz kernel over a locally compact abelian group. . Commentationes Math. , 34 : 153 – 164 .
  • Vinti , G. 1994 . Generalized φ-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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