Illinois Journal of Mathematics

Henstock-Kurzweil Fourier transforms

Erik Talvila

Full-text: Open access

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.

Article information

Source
Illinois J. Math., Volume 46, Number 4 (2002), 1207-1226.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138475

Digital Object Identifier
doi:10.1215/ijm/1258138475

Mathematical Reviews number (MathSciNet)
MR1988259

Zentralblatt MATH identifier
1037.42007

Subjects
Primary: 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Secondary: 26A39: Denjoy and Perron integrals, other special integrals

Citation

Talvila, Erik. Henstock-Kurzweil Fourier transforms. Illinois J. Math. 46 (2002), no. 4, 1207--1226. doi:10.1215/ijm/1258138475. https://projecteuclid.org/euclid.ijm/1258138475


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