Embedded eigenvalues of generalized Schrödinger operators

Abstract

We provide examples of operators $T(D)+V$ in $L^2({\mathbb{R}}^d)$ with decaying potentials that have embedded eigenvalues. The decay of the potential depends on the curvature of the (Fermi) surfaces of constant kinetic energy $T$. We make the connection to counterexamples in Fourier restriction theory.