On the number and sums of eigenvalues of Schr\"odinger-type operators with degenerate kinetic energy

TL;DR

This paper investigates the eigenvalues of Schrödinger-type operators with degenerate kinetic energy, providing estimates for sums of functions of negative eigenvalues using advanced harmonic analysis tools.

Contribution

It introduces new eigenvalue sum estimates for operators with kinetic energy degeneracies on submanifolds, utilizing the Stein-Tomas theorem and its generalizations.

Findings

Derived bounds for sums of negative eigenvalues

Extended Stein-Tomas theorem applications to Schrödinger operators

Enhanced understanding of spectral properties with degenerate kinetic energy

Abstract

We estimate sums of functions of negative eigenvalues of Schr\"odinger-type operators whose kinetic energy vanishes on a codimension one submanifold. Our main technical tool is the Stein-Tomas theorem and some of its generalizations.