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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Construction of orthonormal wavelets using Kampé de Fériet functions
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by Ahmed I. Zayed PDF
Proc. Amer. Math. Soc. 130 (2002), 2893-2904 Request permission

Abstract:

One of the main aims of this paper is to bridge the gap between two branches of mathematics, special functions and wavelets. This is done by showing how special functions can be used to construct orthonormal wavelet bases in a multiresolution analysis setting. The construction uses hypergeometric functions of one and two variables and a generalization of the latter, known as Kampé de Fériet functions. The mother wavelets constructed by this process are entire functions given by rapidly converging power series that allow easy and fast numerical evaluation. Explicit representation of wavelets facilitates, among other things, the study of the analytic properties of wavelets.
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Additional Information
  • Ahmed I. Zayed
  • Affiliation: Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60614
  • Email: azayed@condor.depaul.edu
  • Received by editor(s): November 8, 2000
  • Published electronically: May 1, 2002
  • Communicated by: David R. Larson
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 2893-2904
  • MSC (2000): Primary 42C40, 33C20; Secondary 42C15, 33E20
  • DOI: https://doi.org/10.1090/S0002-9939-02-06690-X
  • MathSciNet review: 1908912