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Berezin Transform for Solvable Groups |
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| Authors: | Jonathan Arazy Harald Upmeier |
| Institution: | (1) Department of Mathematics, University of Haifa, Eshkol Tower, Haifa, 31905, Israel;(2) Fachbereich Mathematik, Universität Marburg, D-35032 Marburg, Germany |
| Abstract: | We study the Berezin transform in the context of solvable groups AN (acting on homogeneous cones and Siegel domains) and determine its spectral decomposition, using an explicit integral kernel representation for the associated  eigen-operators in terms of multivariable hypergeometric functions. |
| Keywords: | Berezin transform solvable groups homogeneous Siegel domains symmetric cones Euclidean Jordan algebras reproducing kernels correspondence principle summability kernels hypergeometric functions |
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