Revista Matemática Iberoamericana

The Singularity of Orbital Measures on Compact Lie Groups

Kathryn E. Hare and Wai Ling Yee

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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.

Article information

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

Dates
First available in Project Euclid: 17 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1087482025

Mathematical Reviews number (MathSciNet)
MR2073130

Zentralblatt MATH identifier
1052.43011

Subjects
Primary: 43A80: Analysis on other specific Lie groups [See also 22Exx]
Secondary: 22E46: Semisimple Lie groups and their representations 43A65: Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]

Keywords
orbital measures compact Lie group characters

Citation

Hare, Kathryn E.; Yee, Wai Ling. The Singularity of Orbital Measures on Compact Lie Groups. Rev. Mat. Iberoamericana 20 (2004), no. 2, 517--530. https://projecteuclid.org/euclid.rmi/1087482025


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References

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