Henstock-Kurzweil Fourier transforms

By Erik Talvila. 2002

49 citations recorded by the source corpus.

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. AMS (MOS) subject classification: 42A38, 26A39

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

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