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arXiv · 2412.18382

Wehrl inequalities for matrix coefficients of holomorphic discrete series

Robin van Haastrecht·Genkai Zhang
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Abstract

We prove Wehrl-type $L^2(G)-L^{p}(G)$ 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.

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Robin van Haastrecht, Genkai Zhang. 2024-12-24. Wehrl inequalities for matrix coefficients of holomorphic discrete series. https://arxiv.org/abs/2412.18382

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