Smoothness of convolution powers of orbital measures on the symmetric space SU(n)/SO(n)

Sanjiv Kumar Gupta, Kathryn E. Hare

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We prove that if μa = mka*mK is the K-bi-invariant measure supported on the double coset K a K {succeeds or equal to} SU (n), for K = SO(n), then μa k is absolutely continuous with respect to the Haar measure on SU(n) for all a not in the normalizer of K if and only if k ≥ n. The measure, μa, supported on the minimal dimension double coset has the property that μa n-1 is singular to the Haar measure.

Original languageEnglish
Pages (from-to)27-43
Number of pages17
JournalMonatshefte fur Mathematik
Volume159
Issue number1
DOIs
Publication statusPublished - 2009

Keywords

  • Absolutely continuous measure
  • Bi-invariant measure
  • SU(n)
  • Symmetric space

ASJC Scopus subject areas

  • Mathematics(all)

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