Spectrum of Hausdorff operators on weighted Bergman and Hardy spaces of the upper half-plane

TL;DR

This paper characterizes the spectrum of Hausdorff operators on weighted Bergman and Hardy spaces in the upper half-plane, providing insights into their spectral properties in complex analysis.

Contribution

It offers a new characterization of the spectrum of Hausdorff operators on specific function spaces in the upper half-plane, advancing understanding in operator theory.

Findings

Spectrum characterized for these operators

Results applicable to weighted Bergman spaces

Insights into spectral behavior in Hardy spaces

Abstract

We characterize the spectrum of Hausdorff operators on weighted Bergman and power weighted Hardy spaces of the upper half-plane.