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

2024/10/30 by Matthew Dawson, Dawson, Matthew, Vishwa Dewage +5 · 1 citation
Mathematics · #22D25 #32A36 #47B35 #47L80 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2410.23110

openalex publication_date 2024/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study quantum harmonic analysis (QHA) on the Bergman space A²(\mathbbBⁿ) over the unit ball in ℂⁿ. We formulate a Wiener's Tauberian theorem, and characterizations of the radial Toeplitz algebra over A²(\mathbbBⁿ). We discuss the α-Berezin transform and investigate the question of approximations by Toeplitz operators.

Cited by

• On quantum large sieve inequalities and operator recovery from incomplete information

Related

• On the density of Toeplitz operators in the Toeplitz algebra over the Bergman space of the unit ball
• Toeplitz algebra of bounded symmetric domains: A quantum harmonic analysis approach via localization
• The Laplacian of an operator and the radial Toeplitz algebra
• Toeplitz operators on generalized harmonic Bergman spaces
• Toeplitz operators on the unit ball with locally integrable symbols