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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 307, Pages 193–211
DOI: https://doi.org/10.4213/tm4061 (Mi tm4061) 		 
The Mellin Transform and the Plancherel Theorem for the Discrete Heisenberg Group

A. N. Parshin

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
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DOI: https://doi.org/10.4213/tm4061
Abstract: In the classical representation theory of locally compact groups, there are well-known constructions of a unitary dual space of irreducible representations, the Fourier transform, and the Plancherel theorem. In this paper, we present analogs of these constructions for the discrete Heisenberg group and its irreducible infinite-dimensional representations in a vector space without topology.
Received: October 28, 2019
Revised: November 23, 2019
Accepted: November 27, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 307, Pages 174–192
DOI: https://doi.org/10.1134/S0081543819060105
Bibliographic databases:
Document Type: Article
UDC: 512.547.4+517.986
Language: Russian
Citation: A. N. Parshin, “The Mellin Transform and the Plancherel Theorem for the Discrete Heisenberg Group”, Algebra, number theory, and algebraic geometry, Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich, Trudy Mat. Inst. Steklova, 307, Steklov Mathematical Institute of RAS, Moscow, 2019, 193–211; Proc. Steklov Inst. Math., 307 (2019), 174–192
Citation in format AMSBIB
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\pages 193--211
\publ Steklov Mathematical Institute of RAS
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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