(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 $f\left(x\right)$ be a boundary variation on R and $f\left(x\right)$® 0 ($x$® ± ¥). Then its Fourier transform

 ^f (l) = (LÙ) +¥óõ-¥ f(t)e-2pilt dt

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

 f(x) = (AÙ) +¥óõ-¥ ^f (l)e2pilx dl.

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