Continuous measures on compact Lie groups

M. Anoussis; A. Bisbas

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 4, page 1277-1296
  • ISSN: 0373-0956

Abstract

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We study continuous measures on a compact semisimple Lie group G using representation theory. In Section 2 we prove a Wiener type characterization of a continuous measure. Next we construct central measures on G which are related to the well known Riesz products on locally compact abelian groups. Using these measures we show in Section 3 that if C is a compact set of continuous measures on G there exists a singular measure ν such that ν * μ is absolutely continuous with respect to the Haar measure on G for every μ in C . In Section 4 we show that if f is a finite linear combination of characters then there exist two singular measures μ and ν on G such that f = μ * ν . In the final section we obtain a Wiener-type characterization of a continuous measure on a symmetric space of compact type G / K .

How to cite

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Anoussis, M., and Bisbas, A.. "Continuous measures on compact Lie groups." Annales de l'institut Fourier 50.4 (2000): 1277-1296. <http://eudml.org/doc/75457>.

@article{Anoussis2000,
abstract = {We study continuous measures on a compact semisimple Lie group $G$ using representation theory. In Section 2 we prove a Wiener type characterization of a continuous measure. Next we construct central measures on $G$ which are related to the well known Riesz products on locally compact abelian groups. Using these measures we show in Section 3 that if $C$ is a compact set of continuous measures on $G$ there exists a singular measure $\nu $ such that $\nu \ast \mu $ is absolutely continuous with respect to the Haar measure on $G$ for every $\mu $ in $C$. In Section 4 we show that if $f$ is a finite linear combination of characters then there exist two singular measures $\mu $ and $\nu $ on $G$ such that $f=\mu \ast \nu $. In the final section we obtain a Wiener-type characterization of a continuous measure on a symmetric space of compact type $G/K$.},
author = {Anoussis, M., Bisbas, A.},
journal = {Annales de l'institut Fourier},
keywords = {compact semisimple Lie group; continuous measures; multipliers},
language = {eng},
number = {4},
pages = {1277-1296},
publisher = {Association des Annales de l'Institut Fourier},
title = {Continuous measures on compact Lie groups},
url = {http://eudml.org/doc/75457},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Anoussis, M.
AU - Bisbas, A.
TI - Continuous measures on compact Lie groups
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 4
SP - 1277
EP - 1296
AB - We study continuous measures on a compact semisimple Lie group $G$ using representation theory. In Section 2 we prove a Wiener type characterization of a continuous measure. Next we construct central measures on $G$ which are related to the well known Riesz products on locally compact abelian groups. Using these measures we show in Section 3 that if $C$ is a compact set of continuous measures on $G$ there exists a singular measure $\nu $ such that $\nu \ast \mu $ is absolutely continuous with respect to the Haar measure on $G$ for every $\mu $ in $C$. In Section 4 we show that if $f$ is a finite linear combination of characters then there exist two singular measures $\mu $ and $\nu $ on $G$ such that $f=\mu \ast \nu $. In the final section we obtain a Wiener-type characterization of a continuous measure on a symmetric space of compact type $G/K$.
LA - eng
KW - compact semisimple Lie group; continuous measures; multipliers
UR - http://eudml.org/doc/75457
ER -

References

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