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arXiv · 2009.09720

Berezin symbols and spectral measures of representation operators

Benjamin Cahen
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Abstract

Let $G$ be a Lie group with Lie algebra $\mathfrak g$ and let $\pi$ be a unitary representation of $G$ realized on a reproducing kernel Hilbert space. We use Berezin quantization to study spectral measures associated with operators $-id\pi(X)$ for $X\in {\mathfrak g}$. As an application, we show how results about contractions of Lie group representations give rise to results on convergence of sequences of spectral measures. We give some examples including contractions of $SU(1,1)$ and $SU(2)$ to the Heisenberg group.

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Benjamin Cahen. 2020-09-21. Berezin symbols and spectral measures of representation operators. https://arxiv.org/abs/2009.09720

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