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

DOI10.1007/BF01196516zbMath0910.43008MaRDI QIDQ1269737

Etsuro Fujita, Takaaki Nomura

Publication date: 15 April 1999

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

Toeplitz operatorspectral decompositionBerezin transformHahn polynomialsmatrix space \(\text{Mat}(2,\mathbb{C})\)Meijer \(G\)-functions

Mathematics Subject Classification ID

Eigenvalue problems for linear operators (47A75) Applications of Lie groups to the sciences; explicit representations (22E70) Linear operators on function spaces (general) (47B38) Integral operators (47G10) Analysis on other specific Lie groups (43A80) Appell, Horn and Lauricella functions (33C65)

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Cites Work

• Wiener-Hopf operators on \(U_2\)
• Bounded \(K\)-spherical functions on Heisenberg groups
• A weighted Plancherel formula. III: The case of the hyperbolic matrix ball
• Spectral decomposition of Berezin transformations on \(C^n\) related to the natural \(U(n)\)-action
• On the decomposition of tensor products of the representations of the classical groups: By means of the universal characters
• The Berezin transform and invariant differential operators
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Special Functions of Matrix Argument. I: Algebraic Induction, Zonal Polynomials, and Hypergeometric Functions
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