Ground States for Nonlocal Schrödinger Type Operators on Locally Compact Abelian Groups

Abstract

We find classes of nonlocal operators of Schrödinger type on a locally compact noncompact Abelian group $G$, for which there exists a ground state. In particular, such a result is obtained for the case where the principal part of our operator generates a recurrent random walk. Explicit conditions for the existence of a ground state are obtained for the case $G={\mathbb{Q}}_p^n$ where ${\mathbb{Q}}_p$ is the field of $p$-adic numbers.

To appear in Journal of Spectral Theory

References in corpus (1)

• Tables of Integrals of Complex-valued Functions of p-Adic arguments