On Hardy's theorem on SU(1, 1)

Takeshi Kawazoe, Jianming Liu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The classical Hardy theorem asserts that f and its Fourier transform f̂ can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU(1, 1) there are infinitely many "good" functions in the sense that f and its spherical Fourier transform f̂ both have good decay. In this paper, we shall characterize such functions on SU(1, 1).

Original languageEnglish
Pages (from-to)429-440
Number of pages12
JournalChinese Annals of Mathematics. Series B
Volume28
Issue number4
DOIs
Publication statusPublished - 2007 Aug

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Hardy's Theorem
Fourier transform
Fourier transforms
Jacobi
Lie groups
Decay
Transform
Theorem

Keywords

  • Heat kernel
  • Jacobi transform
  • Plancherel formula

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On Hardy's theorem on SU(1, 1). / Kawazoe, Takeshi; Liu, Jianming.

In: Chinese Annals of Mathematics. Series B, Vol. 28, No. 4, 08.2007, p. 429-440.

Research output: Contribution to journalArticle

Kawazoe, Takeshi ; Liu, Jianming. / On Hardy's theorem on SU(1, 1). In: Chinese Annals of Mathematics. Series B. 2007 ; Vol. 28, No. 4. pp. 429-440.
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