The smoothness of convolutions of zonal measures on compact symmetric spaces

Sanjiv K. Gupta, Kathryn E. Hare

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We prove that for every irreducible, compact symmetric space, Gc/K, of rank r, the convolution of any (2r+1) continuous, K-bi-invariant measures is absolutely continuous with respect to the Haar measure on Gc. We also prove that the convolution of (r+1) continuous, K-invariant measures on the -1 eigenspace in the Cartan decomposition of the Lie algebra of Gc is absolutely continuous with respect to Lebesgue measure. These results are nearly sharp.

Original languageEnglish
Pages (from-to)668-678
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume402
Issue number2
DOIs
Publication statusPublished - Jun 15 2013

Fingerprint

Compact Space
Symmetric Spaces
Absolutely Continuous
Convolution
Invariant Measure
Smoothness
Haar Measure
Eigenspace
Lebesgue Measure
Algebra
Lie Algebra
Decomposition
Decompose

Keywords

  • Absolutely continuous
  • Double coset
  • Symmetric space
  • Zonal measure

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

The smoothness of convolutions of zonal measures on compact symmetric spaces. / Gupta, Sanjiv K.; Hare, Kathryn E.

In: Journal of Mathematical Analysis and Applications, Vol. 402, No. 2, 15.06.2013, p. 668-678.

Research output: Contribution to journalArticle

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