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
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 journal › Article
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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.
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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 -