Berezin transform for solvable groups
The authors study the Berezin transform for the multi-weighted Bergman spaces \(H^2_\nu(D)=\{h\in L^2(D,d\mu_\nu): h\) holomorphic\} of Gindikin type on homogeneous cones and Siegel domains \(D,\) depending on a vector parameter \(\nu=(\nu_1,\ldots,\nu_r).\) Using an explicit kernel representation for the associated eigen-operators they provide its spectral decomposition.
scientific article; zbMATH DE number 2093652