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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Multidimensional chromatic derivatives and series expansions
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by Aleksandar Ignjatovic and Ahmed I. Zayed PDF
Proc. Amer. Math. Soc. 139 (2011), 3513-3525 Request permission

Abstract:

Chromatic derivatives and series expansions of bandlimited functions have recently been introduced as an alternative representation to the Taylor series, and they have been shown to be more useful in practical signal processing applications than in the Taylor series. Although chromatic series were originally introduced for bandlimited functions, they have now been extended to a larger class of functions. The $n$-th chromatic derivative of an analytic function is a linear combination of the $k$-th ordinary derivatives with $0\leq k\leq n,$ where the coefficients of the linear combination are based on a suitable system of orthogonal polynomials. The goal of this article is to extend chromatic derivatives and series to higher dimensions. This is of interest not only because the associated multivariate orthogonal polynomials have much reacher structure than in the univariate case, but also because we believe that the multidimensional case will find natural applications to fields such as image processing and analysis.
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Additional Information
  • Aleksandar Ignjatovic
  • Affiliation: School of Computer Science and Engineering, University of New South Wales, Sydney, Australia
  • Email: ignjat@cse.unsw.edu.au
  • Ahmed I. Zayed
  • Affiliation: Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60614
  • Email: azayed@condor.depaul.edu
  • Received by editor(s): January 24, 2010
  • Received by editor(s) in revised form: August 24, 2010
  • Published electronically: February 17, 2011
  • Communicated by: Walter Van Assche
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3513-3525
  • MSC (2010): Primary 41A58, 42C15; Secondary 94A12, 94A20
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10789-5
  • MathSciNet review: 2813383