arXiv math/02121052002-12-07math.CA

Henstock--Kurzweil Fourier transforms

Erik Talvila

备注：: To appear in Illinois Journal of Mathematics

英文摘要：

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.

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