\(L^{2}\)-singular dichotomy for orbital measures of classical simple Lie algebras

DOI10.1007/s00209-008-0364-zzbMath1168.43003OpenAlexW2152645333MaRDI QIDQ1014229

Sanjiv Kumar Gupta, Sobhan Seyfaddini, Kathryn E. Hare

Publication date: 27 April 2009

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-008-0364-z

zbMATH Keywords

Lie algebrasorbital measures\(L^2\)-singular dichotomy

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Integration on manifolds; measures on manifolds (58C35) Analysis on other specific Lie groups (43A80)

Related Items (10)

A geometric proof of the \(L^{2}\)-singular dichotomy for orbital measures on Lie algebras and groups ⋮ THE SMOOTHNESS OF ORBITAL MEASURES ON NONCOMPACT SYMMETRIC SPACES ⋮ The absolute continuity of convolutions of orbital measures in \(SO(2n+1)\) ⋮ The smoothness of convolutions of zonal measures on compact symmetric spaces ⋮ CONVOLUTION OF ORBITAL MEASURES IN SYMMETRIC SPACES ⋮ The absolute continuity of convolutions of orbital measures in symmetric spaces ⋮ THE -SINGULAR DICHOTOMY FOR EXCEPTIONAL LIE GROUPS AND ALGEBRAS ⋮ The absolute continuity of convolution products of orbital measures in exceptional symmetric spaces ⋮ Sums of adjoint orbits and \(L^2\)-singular dichotomy for \(SU(m)\) ⋮ \(L^2\)-singular dichotomy for orbital measures of classical compact Lie groups

Cites Work

• Singularity of orbital measures in SU\((n)\)
• Harmonic analysis on nilpotent groups and singular integrals. II: Singular kernels supported on submanifolds
• Norms of characters and Fourier series on compact Lie groups
• Norms of characters and lacunarity for compact Lie groups
• Singularity of orbits in classical Lie algebras
• Harmonic analysis on nilpotent groups and singular integrals. III: Fractional integration along manifolds
• Central measures on compact simple Lie groups
• \(L^ p\)-\(L^ q\) estimates for orbital measures and Radon transforms on compact Lie groups and Lie algebras
• The dichotomy problem for orbital measures of \(SU(n)\)
• On a Relationship Between Adjoint Orbits and Conjugacy Classes of a Lie Group
• Sums of adjoint orbits
• The size of characters of compact Lie groups
• The size of characters of exceptional lie groups
• Operators and Harmonic Analysis on the Sphere
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