On Commutants of Toeplitz Operators with Generalized BiharmonicPoly-Quasihomogeneous Symbols

Abstract

This paper introduces generalized biharmonic poly-quasihomogeneous  functions and studies Toeplitz operators with such symbols on the Bergman space.  We characterize the commutants of these operators and investigate their spectral properties, generalizing previous work on biharmonic and poly quasihomogeneous symbols. We provide comprehensive proofs, examples, and  extend our results to related classes of symbols.