BOEHMIANS ON THE TORUS

Nemzer, Dennis

doi:10.4134/BKMS.2006.43.4.831

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BOEHMIANS ON THE TORUS

Journal title : Bulletin of the Korean Mathematical Society
Volume 43, Issue 4, 2006, pp.831-839
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2006.43.4.831

Title & Authors

BOEHMIANS ON THE TORUS
Nemzer, Dennis;

Abstract

By relaxing the requirements for a sequence of functions to be a delta sequence, a space of Boehmians on the torus ${${\beta}(T^d)$}$ is constructed and studied. The space ${${\beta}(T^d)$}$ contains the space of distributions as well as the space of hyperfunctions on the torus. The Fourier transform is a continuous mapping from ${${\beta}(T^d)$}$ onto a subspace of Schwartz distributions. The range of the Fourier transform is characterized. A necessary and sufficient condition for a sequence of Boehmians to converge is that the corresponding sequence of Fourier transforms converges in ${$D`({\mathbb{R}}^d)$}$ .

Keywords

Boehmian;Fourier transform;distribution;

Language

English

Cited by

3time(s) in CrossRef

An extension of certain integral transform to a space of Boehmians, Journal of the Association of Arab Universities for Basic and Applied Sciences, 2015, 17, 36

On the Generalized Krätzel Transform and Its Extension to Bohemian Spaces, Abstract and Applied Analysis, 2013, 2013, 1

Stockwell transform for Boehmians, Integral Transforms and Special Functions, 2013, 24, 4, 251

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