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math.FA2024
A quantum harmonic analysis approach to the Berger-Coburn theorem
Vishwa Dewage, Mishko Mitkovski
We use quantum harmonic analysis for densely defined operators to provide a simplified proof of the Berger-Coburn theorem for boundedness of Toeplitz operators. In addition, we rev…
math.FA2024
Quantum Harmonic Analysis on the Unweighted Bergman Space of the Unit Ball
Matthew Dawson, Vishwa Dewage, Mishko Mitkovski +1
We study quantum harmonic analysis (QHA) on the Bergman space over the unit ball in . We formulate a Wiener's Tauberian theorem, and cha…
math.FA2024
The Laplacian of an operator and the radial Toeplitz algebra
Vishwa Dewage, Mishko Mitkovski
Using tools from quantum harmonic analysis, we show that the domain of the Laplacian of an operator is dense in the Toeplitz algebra over the Fock space $\mathcal{F}^2(\mathbb{C}^n…