An Application of Value Distribution Theory to Schroedinger Operators with Absolutely Continuous Spectrum

TL;DR

This paper applies value distribution theory to Sturm-Liouville problems to analyze the asymptotic distribution of eigenvalues in Schrödinger operators with absolutely continuous spectrum.

Contribution

It introduces a novel application of value distribution theory to study eigenvalue distribution in Schrödinger operators with continuous spectrum.

Findings

Eigenvalues are shown to be uniformly asymptotically distributed.

The method provides a new approach to spectral analysis of Schrödinger operators.

Results extend understanding of eigenvalue distribution in operators with absolutely continuous spectrum.

Abstract

We use the "Value Distribution" theory developed by Pearson and Breimesser to obtain a sequence of functions in the eigenvalue parameter for some Sturm-Liouville problems which have the property of being "uniformly asymptotically distributed".