Spherical functions and the Fourier algebra

Christopher Meaney

doi:10.1007/BF02924853

Spherical functions and the Fourier algebra

Christopher Meaney^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We show how the inversion formula for the Radon transform of radial functions can be used to demonstrate local regularity for radial Fourier transforms and a similar result for Ad(G)-invariant Fourier transforms on the Lie algebra of a compact semisimple connected Lie group G. We also sketch the description of the bi-K-invariant elements of the Fourier algebra of G as inverse spherical transforms, when (G,K) are a Gel'fand pair.

Original language	English
Pages (from-to)	127-132
Number of pages	6
Journal	Rendiconti del Seminario Matematico e Fisico di Milano
Volume	54
Issue number	1
DOIs	https://doi.org/10.1007/BF02924853
Publication status	Published - Dec 1985
Externally published	Yes

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abstract = "We show how the inversion formula for the Radon transform of radial functions can be used to demonstrate local regularity for radial Fourier transforms and a similar result for Ad(G)-invariant Fourier transforms on the Lie algebra of a compact semisimple connected Lie group G. We also sketch the description of the bi-K-invariant elements of the Fourier algebra of G as inverse spherical transforms, when (G,K) are a Gel'fand pair.",

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AB - We show how the inversion formula for the Radon transform of radial functions can be used to demonstrate local regularity for radial Fourier transforms and a similar result for Ad(G)-invariant Fourier transforms on the Lie algebra of a compact semisimple connected Lie group G. We also sketch the description of the bi-K-invariant elements of the Fourier algebra of G as inverse spherical transforms, when (G,K) are a Gel'fand pair.

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Spherical functions and the Fourier algebra

Abstract

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