L2-Singular Dichotomy for Orbital Measures on Complex Groups
Gupta, S. K. ; Hare, K. E.
Bollettino dell'Unione Matematica Italiana, Tome 3 (2010), p. 409-419 / Harvested from Biblioteca Digitale Italiana di Matematica
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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∈L2 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 GC. 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.

Publié le : 2010-10-01
@article{BUMI_2010_9_3_3_409_0,
     author = {S. K. Gupta and K. E. Hare},
     title = {$L^{2}$-Singular Dichotomy for Orbital Measures on Complex Groups},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {3},
     year = {2010},
     pages = {409-419},
     zbl = {1217.22008},
     mrnumber = {2742774},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2010_9_3_3_409_0}
}

Gupta, S. K.; Hare, K. E. $L^{2}$-Singular Dichotomy for Orbital Measures on Complex Groups. Bollettino dell'Unione Matematica Italiana, Tome 3 (2010) pp. 409-419. http://gdmltest.u-ga.fr/item/BUMI_2010_9_3_3_409_0/

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