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Winter 2002 Henstock-Kurzweil Fourier transforms
Erik Talvila
Illinois J. Math. 46(4): 1207-1226 (Winter 2002). DOI: 10.1215/ijm/1258138475

Abstract

The Fourier transform is considered as a Henstock-Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient conditions are given for it to be continuous. The Riemann-Lebesgue lemma fails: Henstock-Kurzweil Fourier transforms can have arbitrarily large point-wise growth. Convolution and inversion theorems are established. An appendix gives sufficient conditions for interchanging repeated Henstock-Kurzweil integrals and gives an estimate on the integral of a product.

Citation

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Erik Talvila. "Henstock-Kurzweil Fourier transforms." Illinois J. Math. 46 (4) 1207 - 1226, Winter 2002. https://doi.org/10.1215/ijm/1258138475

Information

Published: Winter 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1037.42007
MathSciNet: MR1988259
Digital Object Identifier: 10.1215/ijm/1258138475

Subjects:
Primary: 42A38
Secondary: 26A39

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 4 • Winter 2002
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