Berezin transforms on the 2 × 2 matrix space related to the U(2) × U(2)-action

Etsuro Fujita; Takaaki Nomura

doi:10.1007/BF01196516

Berezin transforms on the 2 × 2 matrix space related to the U(2) × U(2)-action

Etsuro Fujita, Takaaki Nomura

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Abstract

In this paper we establish the spectral decomposition of the Berezin transforms on the space Mat(2, ℂ) of complex 2 × 2 matrices related to the two-sided action of U(2) × U(2). The eigenspaces are described explicitly by means of the matrix elements of a certain representation of GL(2, ℂ) and each eigenvalue is expressed as a finite sum involving the Meijer G-functions evaluated at 1 and the Hahn polynomials.

Original language	English
Pages (from-to)	152-179
Number of pages	28
Journal	Integral Equations and Operator Theory
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/BF01196516
Publication status	Published - Jan 1 1998
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory

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10.1007/BF01196516

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abstract = "In this paper we establish the spectral decomposition of the Berezin transforms on the space Mat(2, ℂ) of complex 2 × 2 matrices related to the two-sided action of U(2) × U(2). The eigenspaces are described explicitly by means of the matrix elements of a certain representation of GL(2, ℂ) and each eigenvalue is expressed as a finite sum involving the Meijer G-functions evaluated at 1 and the Hahn polynomials.",

author = "Etsuro Fujita and Takaaki Nomura",

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N2 - In this paper we establish the spectral decomposition of the Berezin transforms on the space Mat(2, ℂ) of complex 2 × 2 matrices related to the two-sided action of U(2) × U(2). The eigenspaces are described explicitly by means of the matrix elements of a certain representation of GL(2, ℂ) and each eigenvalue is expressed as a finite sum involving the Meijer G-functions evaluated at 1 and the Hahn polynomials.

AB - In this paper we establish the spectral decomposition of the Berezin transforms on the space Mat(2, ℂ) of complex 2 × 2 matrices related to the two-sided action of U(2) × U(2). The eigenspaces are described explicitly by means of the matrix elements of a certain representation of GL(2, ℂ) and each eigenvalue is expressed as a finite sum involving the Meijer G-functions evaluated at 1 and the Hahn polynomials.

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ER -

Berezin transforms on the 2 × 2 matrix space related to the U(2) × U(2)-action

Abstract

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