### 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 | |

Publication status | Published - Jan 1 1998 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Algebra and Number Theory

### Cite this

*Integral Equations and Operator Theory*,

*32*(2), 152-179. https://doi.org/10.1007/BF01196516

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

Research output: Contribution to journal › Article

*Integral Equations and Operator Theory*, vol. 32, no. 2, pp. 152-179. https://doi.org/10.1007/BF01196516

}

TY - JOUR

T1 - Berezin transforms on the 2 × 2 matrix space related to the U(2) × U(2)-action

AU - Fujita, Etsuro

AU - Nomura, Takaaki

PY - 1998/1/1

Y1 - 1998/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=0032193571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032193571&partnerID=8YFLogxK

U2 - 10.1007/BF01196516

DO - 10.1007/BF01196516

M3 - Article

AN - SCOPUS:0032193571

VL - 32

SP - 152

EP - 179

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 2

ER -