Henstock–Kurzweil Fourier transforms
نویسنده
چکیده
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. 2000 subject classification: 42A38, 26A39
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