Weyl's law under minimal assumptions

TL;DR

This paper demonstrates that Weyl's law applies to Schrödinger operators with minimal assumptions on potentials and domains, broadening its applicability in spectral theory.

Contribution

It establishes the validity of Weyl's law under minimal conditions on potentials, vector potentials, and domains for Schrödinger operators.

Findings

Weyl's law holds under minimal assumptions.

Applicability extends to broader classes of Schrödinger operators.

Results include the behavior of eigenvalues and Riesz means.

Abstract

We show that Weyl's law for the number and the Riesz means of negative eigenvalues of Schr\"odinger operators remains valid under minimal assumptions on the potential, the vector potential and the underlying domain.