Asymptotics of the Weyl Function for Schr\"odinger Operators with Measure-Valued Potentials

TL;DR

This paper derives a generalized asymptotic expansion for the Weyl function of one-dimensional Schrödinger operators with measure-valued potentials, extending classical results and interpreting them in the distributional sense.

Contribution

It introduces a new asymptotic expansion for the Weyl function applicable to measure-valued potentials, broadening classical Schrödinger operator analysis.

Findings

Generalized asymptotic expansion for Weyl function

Extension of classical Atkinson formula

Distributional interpretation of asymptotics

Abstract

We derive an asymptotic expansion for the Weyl function of a one-dimensional Schr\"odinger operator which generalizes the classical formula by Atkinson. Moreover, we show that the asymptotic formula can also be interpreted in the sense of distributions.