Quantum Harmonic Analysis (QHA): In 1984, R. Werner introduced QHA in his paper titled "Quantum harmonic analysis on the phase space".  He defined and studied convolutions of functions and operators as well as convolutions between two operators. The Wiener's Tauberian theorem for operators is also discussed. By now,  QHA has many applications in several areas of mathematics, including time-frequency analysis, mathematical physics, and operator theory. As observed by Fulsche, QHA is well-suited to study Toeplitz operators on the Fock space. 

My research: I use QHA to explore Toeplitz operators on the Fock space.  I am interested in questions such as

1. Commutative Toeplitz algebras and their Gelfand theory

2. Approximations by Toeplitz operators

3. Boundedness of Toeplitz operators

I am also interested in extending the applicability of QHA, in the context of Toeplitz operators, beyond Fock spaces.

1. V. Dewage, Toeplitz algebra of bounded symmetric domains: A quantum harmonic analysis approach via localization. arXiv link 

2. V. Dewage, M. Mitkovski,  On the density of Toeplitz operators in the Toeplitz algebra over the Bergman space of the unit ball. arXiv link 

3. V. Dewage, M. Mitkovski,  A quantum harmonic analysis approach to the Berger-Coburn theorem. arXiv link  (To appear in N.Y.J. Math)

4. M. Dawson, V. Dewage, M. Mitkovski, G. Olafsson, Quantum Harmonic Analysis on the Unweighted Bergman Space of the Unit Ball. arXiv link (To appear in Intgr. equ. oper. theory)

5. V. Dewage, M. Mitkovski, The Laplacian of an operator and the radial Toeplitz algebra. J. Math. Anal. Appl. 547  (1), paper no. 129245 (2025) arXiv link 

6. V. Dewage, M. Mitkovski, Density of Toeplitz operators in rotation-invariant Toeplitz algebras. arXiv link 

7. V. Dewage, G. Olafsson, Toeplitz operators on the Fock space with quasi-radial symbols. Complex Anal. Oper. Theory 16 (4), Paper no. 61, 32 pp. (2022) arXiv link 

At Clemson University

• Fall 2024 - Math 1010 - Essential Mathematics for the Informed Society (2 sections)

• Spring 2024 - Math 4540 - Advanced Calculus II

• Fall 2023 - Math 4350 - Complex Analysis

• Fall 2023 - Math 4630 - Real Analysis

• 2022-2024 - Math 3110 - Linear Algebra (6 sections)

At Louisiana State University

• Spring 2022 - Math 1021 - College Algebra

• Fall 2021 - Math 1550 - Analytic Geometry & Calculus - I

• Summer 2021 - Math 1552 - Analytic Geometry & Calculus - II (75-99% Web based)

• Spring 2021 Math 1550 - Analytic Geometry & Calculus - I (100% Web based)

• Fall 2020 - Math 1021 - College Algebra (100% Web based)

• Summer 2019 - Math 2057 - Multidimensional Calculus

• Summer 2018 - Math 1552 - Analytic Geometry & Calculus - II

• Fall 2017 - Math 1021 - College Algebra