Wehrl Inequalities for Matrix Coefficients of Holomorphic Discrete Series
Journal article, 2026
Let G be a Hermitian Lie group. We prove Wehrl-type L2(G)-Lp(G) inequalities for matrix coefficients of vector-valued holomorphic discrete series of G, for even integers p=2n. The optimal constant is expressed in terms of Harish-Chandra formal degrees for the discrete series. We prove the maximizers are precisely the reproducing kernels.
Matrix coefficients
Lp-spaces
Unitary representations
Lie groups
Reproducing kernels
Toeplitz operators
Hermitian symmetric spaces
Harish-Chandra formal degree
Wehrl inequality
Holomorphic discrete series
Author
Robin van Haastrecht
Chalmers, Mathematical Sciences, Analysis and Probability Theory
University of Gothenburg
Genkai Zhang
Chalmers, Mathematical Sciences, Analysis and Probability Theory
University of Gothenburg
Journal of Geometric Analysis
1050-6926 (ISSN)
Vol. 36 10 324Subject Categories (SSIF 2025)
Probability Theory and Statistics
Mathematical Analysis
DOI
10.1007/s12220-026-02573-z