FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 2, PAGES 351-357

Application of the $A$Ù-integration for Fourier transforms

A. Anter

Abstract

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The following theorem is proved

Theorem. Let the function $f(x)$ be a boundary variation on $$R and $f(x)$® 0 ($x$® ± ¥). Then its Fourier transform

exists in case of $$l ¹ 0 and $f(x)$ recovers by its Fourier transforms by mean of the $A$Ù-integral. Further for all $\$\; x\backslash in\; \backslash tilde\; \{A\}\; \$$, where $f(x)=(1/2)(f(x+0)+f(x-0))$ (for all $x$, except countable subset) the following holds

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Last modified: January 13, 2000