Function-Operator Convolution Algebra on Bergman Space

This paper explores the algebraic structure formed by radial functions and operators on the Bergman space, using a convolution product from quantum harmonic analysis. The focus is on understanding the Gelfand theory of this algebra and the associated Fourier transform of operators. This research contributes to the understanding of operator algebras and harmonic analysis on the Bergman space, potentially providing new tools for analyzing operators and functions in this context.

• •Investigates a commutative Banach algebra formed by radial functions and operators on the Bergman space.
• •Uses a convolution product from quantum harmonic analysis.
• •Focuses on the Gelfand theory of the algebra.
• •Studies the Fourier transform of operators arising from the Gelfand transform.