On the Plancherel measure for linear Lie groups of rank one

DOI10.1007/BF01303630zbMath0426.43010WikidataQ115393721 ScholiaQ115393721MaRDI QIDQ1136023

Roberto J. Miatello

Publication date: 1979

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/154663

zbMATH Keywords

Plancherel measureheat kernel

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30) Analysis on other specific Lie groups (43A80)

Related Items (16)

Gamma factors and Plancherel measures ⋮ Analytic torsion and Ruelle zeta functions for hyperbolic manifolds with cusps ⋮ The wave kernel for the Laplacian on the classical locally symmetric spaces of rank one, theta functions, trace formulas and the Selberg zeta function. With an appendix by Andreas Juhl ⋮ The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps ⋮ Torsion and closed geodesics on complex hyperbolic manifolds ⋮ Resonances of the Laplace operator on homogeneous vector bundles on symmetric spaces of real rank-one ⋮ Selberg and Ruelle zeta functions for non-unitary twists ⋮ Von Neumann spectra near the spectral gap ⋮ Residue representations -- the rank one case ⋮ Harmonic analysis for differential forms on complex hyperbolic spaces ⋮ Regularity of the eta function on manifolds with cusps ⋮ On the first Betti numbers of hyperbolic surfaces ⋮ Von Neumann spectra near zero ⋮ Operator Product on Locally Symmetric Spaces of Rank One and the Multiplicative Anomaly ⋮ A factorization of the Selberg zeta function attached to a rank 1 space form ⋮ Functional equations of Selberg and Ruelle zeta functions for non-unitary twists

Cites Work

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• On the Plancherel formulas for some types of simple Lie groups
• Intertwining operators for semisimple groups
• Erratum to "The Minakshisundaram-Pleijel Coefficients for the Vector Valued Heat Kernel on Compact Locally Symmetric Spaces of Negative Curvature"
• Invariant polynomials and zonal spherical functions

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