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A distribution space for Fourier transform

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Abstract

A space

is constructed and some characterizations of space

are given. It is shown that the classical Fourier transform is extended to the distribution space

, which can be embedded into the Schwartz distribution space

continuously. It is also shown that

is the biggest embedded subspace of

on which the extended Fourier transform,

, is a homeomorphism of

onto itself.

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Author information

Authors and Affiliations

  1. School of Mathematics and Computing Science, Sun Yat-sen University, Guangzhou, 510275, China

    Zhou Chaoying, Yang Lihua & Huang Daren

Authors
  1. Zhou Chaoying
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  2. Yang Lihua
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  3. Huang Daren
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Additional information

Supported by NNSF of China (60475042, 10631080).

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Zhou, C., Yang, L. & Huang, D. A distribution space for Fourier transform. Appl. Math. Chin. Univ. 22, 229–234 (2007). https://doi.org/10.1007/s11766-007-0212-7

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  • DOI: https://doi.org/10.1007/s11766-007-0212-7

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