From spectral theory to bounds on zeros of holomorphic functions

TL;DR

This paper demonstrates how eigenvalue estimates for linear operators can be utilized to derive new bounds on the zeros of holomorphic functions within the unit disk, connecting spectral theory with complex analysis.

Contribution

It introduces a novel approach linking spectral theory to bounds on zeros of holomorphic functions, providing new Blaschke type estimates.

Findings

Eigenvalue estimates lead to improved zero bounds

New Blaschke type bounds are established

Spectral methods are effective in complex analysis

Abstract

We show how eigenvalue estimates for linear operators can be used to obtain new Blaschke type bounds on zeros of holomorphic functions on the unit disk.