On the Cauchy transform vanishing outside a compact

TL;DR

This paper generalizes the F. and M. Riesz Theorem motivated by holomorphic dynamics, exploring conditions under which the Cauchy transform vanishes outside a compact set.

Contribution

It introduces a new generalization of the F. and M. Riesz Theorem tailored for applications in holomorphic dynamics.

Findings

Established conditions for the vanishing of the Cauchy transform outside a compact

Extended classical results to broader contexts in complex analysis

Provided insights relevant to holomorphic dynamics

Abstract

Motivated by a problem in holomorphic dynamics, we present a certain generalization of the celebrated F. and M. Riesz Theorem.