Some Conditions for Existence and Integrability of the Fourier Transform

Details Some Conditions for Existence and Integrability of the Fourier Transform Some Conditions for Existence and Integrability of the Fourier Transform

1995-03-22

arxiv.org/abs/funct-an/9503001v2

Mathematics

Functional Analysis

33 pages, AMSTEX, no figures

Scientific paper

The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions. The Fourier transform is calculated as an improper integral and the limit coincides with the Fourier transform in the distributional sense. The inverse Fourier formula is proved as well. Given are some applications of the result obtained.

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