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

Etsuro Fujita, Takaaki Nomura

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)152-179
Number of pages28
JournalIntegral Equations and Operator Theory
Volume32
Issue number2
DOIs
Publication statusPublished - Jan 1 1998
Externally publishedYes

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Berezin Transform
Meijer's G-function
Hahn Polynomials
Spectral Decomposition
Eigenspace
Eigenvalue

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory

Cite this

Berezin transforms on the 2 × 2 matrix space related to the U(2) × U(2)-action. / Fujita, Etsuro; Nomura, Takaaki.

In: Integral Equations and Operator Theory, Vol. 32, No. 2, 01.01.1998, p. 152-179.

Research output: Contribution to journalArticle

Fujita, Etsuro ; Nomura, Takaaki. / Berezin transforms on the 2 × 2 matrix space related to the U(2) × U(2)-action. In: Integral Equations and Operator Theory. 1998 ; Vol. 32, No. 2. pp. 152-179.
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