Finite Rank Toeplitz Operators: Some Extensions of D.Luecking's Theorem

TL;DR

This paper extends D.Luecking's theorem on finite rank Bergman-Toeplitz operators to include weights as distributions with compact support and to harmonic function spaces, broadening the theorem's applicability.

Contribution

It introduces new extensions of D.Luecking's theorem to more general weights and harmonic function spaces, expanding the theoretical framework.

Findings

Extended theorem to weights as distributions with compact support

Generalized results to harmonic function spaces

Broadened understanding of finite rank Toeplitz operators

Abstract

The recent theorem by D.Luecking about finite rank Bergman-Toeplitz operators is extended to weights being distributions with compact support and to the spaces of harmonic functions.