The Singularity of Orbital Measures on Compact Lie Groups



Revista Matemática Iberoamericana

The Singularity of Orbital Measures on Compact Lie Groups

Kathryn E. Hare and Wai Ling Yee

Source: Rev. Mat. Iberoamericana Volume 20, Number 2 (2004), 517-530.

Abstract

We find the minimal real number $k$ such that the $k$th power of the Fourier transform of any continuous, orbital measure on a classical, compact Lie group belongs to $l^{2}$. This results from an investigation of the pointwise behaviour of characters on these groups. An application is given to the study of $L^{p}$-improving measures.

Primary Subjects: 43A80
Secondary Subjects: 22E46, 43A65
Keywords: orbital measures; compact Lie group; characters

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rmi/1087482025
Zentralblatt MATH identifier: 02110197
Mathematical Reviews number (MathSciNet): MR2073130

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