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A self-contained approach to mellin transform analysis for square integrable functions; applications

A self-contained approach to mellin transform analysis for square integrable functions; applications In several papers the authors introduced a self-contained approach (independent of Fourier or Laplace transform theory) to classical Mellin transform theory as well as to a new finite Mellin transform in case the functions in question are absolutely (Lebesgue) integrable. In this paper the matter is considered for functions which are basically square-integrable. The unified and systematic approach presented, which is valid under minimal and natural hypotheses, is applied to sampling analysis, particularly to that connected with Kramer's lemma. An application is a clean approach to exponential sampling theory (of optical circles) for signals which possess certain integral representations, but also for Mellin-bandlimited signals as well as for those which are only approximately Mellin-bandlimited. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Integral Transforms and Special Functions Taylor & Francis

A self-contained approach to mellin transform analysis for square integrable functions; applications

24 pages

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References (12)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1476-8291
eISSN
1065-2469
DOI
10.1080/10652469908819226
Publisher site
See Article on Publisher Site

Abstract

In several papers the authors introduced a self-contained approach (independent of Fourier or Laplace transform theory) to classical Mellin transform theory as well as to a new finite Mellin transform in case the functions in question are absolutely (Lebesgue) integrable. In this paper the matter is considered for functions which are basically square-integrable. The unified and systematic approach presented, which is valid under minimal and natural hypotheses, is applied to sampling analysis, particularly to that connected with Kramer's lemma. An application is a clean approach to exponential sampling theory (of optical circles) for signals which possess certain integral representations, but also for Mellin-bandlimited signals as well as for those which are only approximately Mellin-bandlimited.

Journal

Integral Transforms and Special FunctionsTaylor & Francis

Published: Dec 1, 1999

Keywords: Mellin transforms for square integrable functions; Mellin translation and convolution; finite Mellin transforms; Mellin-Fourier series; Mellin-Kramer sampling theory; exponential sampling; Primary: 45A15; 44-02; 44-03; Secondary: 47E05; 35K05

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