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arXiv · 2410.23110

Quantum Harmonic Analysis on the Unweighted Bergman Space of the Unit Ball

Matthew Dawson·Vishwa Dewage·Mishko Mitkovski·Gestur Olafsson
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Abstract

We study quantum harmonic analysis (QHA) on the Bergman space $\mathcal{A}^2(\mathbb{B}^n)$ over the unit ball in $\mathbb{C}^n$. We formulate a Wiener's Tauberian theorem, and characterizations of the radial Toeplitz algebra over $\mathcal{A}^2(\mathbb{B}^n)$. We discuss the $\alpha$-Berezin transform and investigate the question of approximations by Toeplitz operators.

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Matthew Dawson, Vishwa Dewage, Mishko Mitkovski, Gestur Olafsson. 2024-10-30. Quantum Harmonic Analysis on the Unweighted Bergman Space of the Unit Ball. https://arxiv.org/abs/2410.23110

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