Uncertainty principles for the jacobi transform

Takeshi Kawazoe

研究成果: Article

1 引用 (Scopus)

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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.

元の言語English
ページ(範囲)127-146
ページ数20
ジャーナルTokyo Journal of Mathematics
31
発行部数1
DOI
出版物ステータスPublished - 2008 1 1

ASJC Scopus subject areas

  • Mathematics(all)

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