Operational calculus for the Fourier transform on the group \(\mathrm{GL}(2,\mathbb{R})\) and the problem about the action of an overalgebra in the Plancherel decomposition

DOI10.1007/s10688-018-0228-1zbMath1408.22014arXiv1801.09398OpenAlexW3100913466MaRDI QIDQ1755981

Yuriĭ A. Neretin

Publication date: 11 January 2019

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.09398

zbMATH Keywords

unitary representationHeisenberg algebrasemisimple Lie groupWeil representationoperational calculusdifferential-difference operatorFourier transform on groupsprincipal series of representations

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (1)

Fourier transform on the Lobachevsky plane and operational calculus

Cites Work

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• Poisson and Fourier transforms for tensor products
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• Some properties of the Fourier transform on semi-simple Lie groups. I
• Canonical representations and overgroups for hyperboloids
• Plancherel formula for Berezin deformation of \(L^{2}\) on Riemannian symmetric space
• After Plancherel formula
• Canonical representations on Lobachevsky spaces: An interaction with an overalgebra
• The action of an overalgebra on the Plancherel decomposition and shift operators in the imaginary direction
• Plancherel Formula for the 2 × 2 Real Unimodular Group
• Pseudo-Riemannian symmetric spaces: Uniform realizations and open embeddings into Grassmannians

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