Poisson and Fourier transforms for tensor products

DOI10.1007/s10688-015-0116-xzbMath1342.22024OpenAlexW2277177484MaRDI QIDQ280795

Vladimir F. Molchanov

Publication date: 10 May 2016

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

Full work available at URL: https://doi.org/10.1007/s10688-015-0116-x

zbMATH Keywords

Fourier transformrepresentationLie algebraLie grouptensor productPoisson transform

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (5)

Poisson Transforms for Tensor Products in Compact Picture ⋮ The Fourier transform on the group \(\mathrm{GL}_2(\mathbb{R})\) and the action of the overalgebra \(\mathfrak{gl}_4\) ⋮ 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 ⋮ Restriction of representations of \(\mathrm{GL}(n + 1, \mathbb{C})\) to \(\mathrm{GL}(n, \mathbb{C})\) and action of the Lie overalgebra ⋮ Fourier transform on the Lobachevsky plane and operational calculus

Cites Work

• Canonical representations and overgroups for hyperboloids
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• Canonical representations on Lobachevsky spaces: An interaction with an overalgebra
• Canonical representations and overgroups for hyperboloids of one sheet and Lobachevsky spaces
• The action of an overalgebra on the Plancherel decomposition and shift operators in the imaginary direction
• Unitary Representations of the Homogeneous Lorentz Group in an O(2, 1) Basis
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