L2- Singular dichotomy for orbital measures on complex groups

S. K. Gupta, K. E. Hare

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

It is known that all continuous orbital measures, μ,on a compact, connected, classical simple Lie group G or its Lie algebra satisfy a dichotomy: either μk εL2 or μk is purely singular to Haar measure. In this note we prove that the same dichotomy holds for the dual situation, continuous orbital measures on the complex group G C. We also determine the sharp exponent k such that any k-fold convolution product of continuous G-bi-invariant measures on GC is absolute continuous with respect to Haar measure.

Original languageEnglish
Pages (from-to)409-419
Number of pages11
JournalBolletino dell Unione Matematica Italiana
Volume3
Issue number3
Publication statusPublished - 2010

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Dichotomy
Haar Measure
Convolution Product
Simple group
Invariant Measure
Lie Algebra
Fold
Exponent

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

L2- Singular dichotomy for orbital measures on complex groups. / Gupta, S. K.; Hare, K. E.

In: Bolletino dell Unione Matematica Italiana, Vol. 3, No. 3, 2010, p. 409-419.

Research output: Contribution to journalArticle

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