The function-operator convolution algebra over the Bergman space of the ball and its Gelfand theory
Functional Analysis
2026-01-01 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2512.24746,
title = {The function-operator convolution algebra over the Bergman space of the ball and its Gelfand theory},
author = {Vishwa Dewage and Robert Fulsche and Gestur Ólafsson},
journal= {arXiv preprint arXiv:2512.24746},
year = {2026}
}
Comments
36 pages