Abstract Plancherel theorems and a Frobenius reciprocity theorem

DOI10.1016/0022-1236(75)90023-3zbMath0305.22016OpenAlexW1991758922MaRDI QIDQ1217210

Richard C. Penney

Publication date: 1975

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(75)90023-3

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30)

Related Items (22)

Finite multiplicity theorems for induced representations of semisimple Lie groups and their applications to generalized Gelfand-Graev representations ⋮ Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula ⋮ The principal series for a reductive symmetric space. I. $H$-fixed distribution vectors ⋮ Modules simples sur une algèbre de Lie nilpotente contenant un vecteur propre pour une sous-algèbre ⋮ Monomial representations of certain exponential Lie groups ⋮ A unified approach to concrete Plancherel theory of homogeneous spaces ⋮ Unnamed Item ⋮ A proof of the polynomial conjecture for nilpotent Lie groups monomial representations ⋮ Analysis of the anomalous diffusion in comb structure with absorbing boundary conditions ⋮ Extensions of positive definite integral kernels on the Heisenberg group ⋮ On the Spectra of Compact Nilmanifolds ⋮ Plancherel theory for real spherical spaces: Construction of the Bernstein morphisms ⋮ Frobenius Reciprocity and Extensions of Nilpotent Lie Groups ⋮ Holomorphically induced representations of some solvable Lie groups ⋮ Distributions of positive type and representations of Lie groups ⋮ Spherical distributions on nilmanifolds ⋮ Spectral decomposition of invariant differential operators on certain nilpotent homogeneous spaces ⋮ The Penney-Fujiwara Plancherel formula for Gelfand pairs ⋮ Analyse harmonique sur les espaces symétriques nilpotents ⋮ Semi-invariant vectors associated with holomorphically induced representations of exponential Lie groups ⋮ Group algebras with a unique C*-norm ⋮ Multiplicité un pour les espaces symétriques exponentiels

Cites Work

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• Integrability of Fourier transforms for unimodular Lie groups
• On \(C^\infty\)-vectors and intertwining bilinear forms for representations of Lie groups
• On rings of operators. III
• Induced Representations of Locally Compact Groups and Applications
• Complex Fourier Analysis on a Nilpotent Lie Group
• Unitary representations of solvable Lie groups
• The plancherel formula for group extensions
• Decomposition of the L 2 -Space of a General Compact Nilmanifold
• On Induced Representations

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