Revista Matemática Iberoamericana

The Singularity of Orbital Measures on Compact Lie Groups

Kathryn E. Hare and Wai Ling Yee

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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

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

First available in Project Euclid: 17 June 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

orbital measures compact Lie group characters


Hare, Kathryn E.; Yee, Wai Ling. The Singularity of Orbital Measures on Compact Lie Groups. Rev. Mat. Iberoamericana 20 (2004), no. 2, 517--530.

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