Uncertainty principles for the jacobi transform

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Abstract

We obtain some uncertainty inequalities for the Jacobi transform fα,β (λ), where we suppose α, β ∈ R and ρ = α +β +1 ≥ 0. As in the Euclidean case, analogues of the local and global uncertainty principles hold for fα,β. In this paper, we shall obtain a new type of an uncertainty inequality and its equality condition: When β ≤ 0 or β ≤ α, the L2-norm of fα,β (λ)λ is estimated below by the L2-norm of ρf (x)(cosh x)−1. Otherwise, a similar inequality holds. Especially, whenβ > α+1, the discrete part of f appears in the Parseval formula and it influences the inequality. We also apply these uncertainty principles to the spherical Fourier transform on SU(1, 1). Then the corresponding uncertainty principle depends, not uniformly on the K-types of f.

Original languageEnglish
Pages (from-to)127-146
Number of pages20
JournalTokyo Journal of Mathematics
Volume31
Issue number1
DOIs
Publication statusPublished - 2008 Jan 1

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Uncertainty Principle
Jacobi
Transform
Norm
Uncertainty
Fourier transform
Euclidean
Equality
Analogue

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Uncertainty principles for the jacobi transform. / Kawazoe, Takeshi.

In: Tokyo Journal of Mathematics, Vol. 31, No. 1, 01.01.2008, p. 127-146.

Research output: Contribution to journalArticle

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