On the number and sums of eigenvalues of Schrödinger-type operators with degenerate kinetic energy

Abstract

We estimate sums of functions of negative eigenvalues of Schrödinger-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.

References updated; Improved Lieb-Thirring and Cwikel-Lieb-Rosenbljum inequalities (Corollary 3.3 and Theorems 3.4 and 3.8) and alternative proof for Theorem 3.4

References in corpus (3)

• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials