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Representations of SU(2,1) in Fourier term modules

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Representations of SU(2,1) in Fourier term modules/ by Roelof W. Bruggeman, Roberto J. Miatello.
Author:	Bruggeman, Roelof W.
other author:	Miatello, Roberto J.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	xi, 210 p. :ill. (chiefly color), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Fourier analysis. -
Online resource:	https://doi.org/10.1007/978-3-031-43192-0
ISBN:	9783031431920

Representations of SU(2,1) in Fourier term modules
Bruggeman, Roelof W.

Representations of SU(2,1) in Fourier term modules[electronic resource] /by Roelof W. Bruggeman, Roberto J. Miatello. - Cham :Springer Nature Switzerland :2023. - xi, 210 p. :ill. (chiefly color), digital ;24 cm. - Lecture notes in mathematics,v. 23401617-9692 ;. - Lecture notes in mathematics ;1943..

This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the "abelian" Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the "non-abelian" modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.

ISBN: 9783031431920

Standard No.: 10.1007/978-3-031-43192-0doiSubjects--Topical Terms:

639284
Fourier analysis.

LC Class. No.: QA403.5

Dewey Class. No.: 515.2433

Representations of SU(2,1) in Fourier term modules
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520 $a This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the "abelian" Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the "non-abelian" modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.
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