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Vishwa Dewage

Publications and source records attributed to Vishwa Dewage.

8 recordsLinked to original sources
arXiv2025

The function-operator convolution algebra over the Bergman space of the ball and its Gelfand theory

We investigate the structure of the commutative Banach algebra formed as the direct sum of integrable radial functions on the disc and the radial operators on the Bergman space, endowed with the convolution from quantum harmonic analysis as the product. In particular, we study the Gelfand theory of this algebra and discuss certain properties of the appropriate Fourier transform of operators which naturally arises from the Gelfand transform.

math.FA↗
arXiv2025

A quantum harmonic analysis approach to the Berger-Coburn theorem

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 revisit compactness and Schatten-class membership of densely defined Toeplitz operators.

math.FA↗
arXiv2025

Toeplitz algebra of bounded symmetric domains: A quantum harmonic analysis approach via localization

We prove that Toeplitz operators are norm dense in the Toeplitz algebra $\mathfrak{T}(L^\infty)$ over the weighted Bergman space $\mathcal{A}^2_ν(Ω)$ of a bounded symmetric domain $Ω\subset\mathbb{C}^n$. Our methods use representation theory, quantum harmonic analysis, and weakly-localized operators. Additionally, we note that the set of all $α$-weakly-localized operators form a self-adjoint algebra, containing the set of all Toeplitz operators, whose norm closure coincides with the Toeplitz algebra.

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arXiv2025

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

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 $α$-Berezin transform and investigate the question of approximations by Toeplitz operators.

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arXiv2024

The Laplacian of an operator and the radial Toeplitz algebra

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 $\mathcal{F}^2(\mathbb{C}^n)$. As an application, we provide a simplified treatment of the Gelfand theory of the radial Toeplitz algebra.

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arXiv2023

Density of Toeplitz operators in rotation-invariant Toeplitz algebras

We use results and techniques from Werner's ``quantum harmonic analysis'' to show that $G$-invariant Toeplitz operators are norm dense in $G$-invariant Toeplitz algebras for all subgroups $G$ of the affine unitary group $U_n\ltimes \mathbb{C}^n$. Additionally, we prove that the quasi-radial Toeplitz operators are dense in the quasi-radial Toeplitz algebra over the Bergman space $\mathcal{A}^2(\mathbb{B}^n)$ and provide a constructive proof of SOT density of Toeplitz operators in the space of all bounded operators.

math.OA↗
arXiv2021

Toeplitz operators on the Fock space with quasi-radial symbols

The Fock space $\mathcal{F}(\mathbb{C}^n)$ is the space of holomorphic functions on $\mathbb{C}^n$ that are square-integrable with respect to the Gaussian measure on $\mathbb{C}^n$. This space plays an important role in several subfields of analysis and representation theory. In particular, it has for a long time been a model to study Toeplitz operators. Esmeral and Maximenko showed in 2016 that radial Toeplitz operators on $\mathcal{F}(\mathbb{C})$ generate a commutative $C^*$-algebra which is isometrically isomorphic to the $C^*$-algebra $C_{b,u}(\mathbb{N}_0,ρ_1)$. In this article, we extend the result to $k$-quasi-radial symbols acting on the Fock space $\mathcal{F}(\mathbb{C}^n)$. We calculate the spectra of the said Toeplitz operators and show that the set of all eigenvalue functions is dense in the $C^*$-algebra $C_{b,u}(\mathbb{N}_0^k,ρ_k)$ of bounded functions on $\mathbb{N}_0^k$ which are uniformly continuous with respect to the square-root metric. In fact, the $C^*$-algebra generated by Toeplitz operators with quasi-radial symbols is $C_{b,u}(\mathbb{N}_0^k,ρ_k)$.

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