Fourier transform on the Lobachevsky plane and operational calculus

DOI10.1134/S001626632004005XMaRDI QIDQ2038440

Yuriĭ A. Neretin

Publication date: 7 July 2021

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

Full work available at URL: https://arxiv.org/abs/2006.11581

zbMATH Keywords

differential-difference operatorsPlancherel decompositiongroup \(\operatorname{SL}(2, \mathbb{R})\)representations of principal series

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46)

Cites Work

• Poisson and Fourier transforms for tensor products
• Difference Sturm-Liouville problems in the imaginary direction
• The Fourier transform on the group \(\mathrm{GL}_2(\mathbb{R})\) and the action of the overalgebra \(\mathfrak{gl}_4\)
• Canonical representations and overgroups for hyperboloids
• Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit
• 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
• A pair of commuting hypergeometric operators on the complex plane and bispectrality
• 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
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