Ground states for nonlocal Schrödinger type operators on locally compact abelian groups
Anatoly N. Kochubei
National Academy of Sciences of Ukraine, Kyiv, UkraineYuri Kondratiev
Universität Bielefeld, Germany
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Abstract
We find classes of nonlocal operators of Schrödinger type on a locally compact noncompact Abelian group , 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 where is the field of -adic numbers.
Cite this article
Anatoly N. Kochubei, Yuri Kondratiev, Ground states for nonlocal Schrödinger type operators on locally compact abelian groups. J. Spectr. Theory 10 (2020), no. 3, pp. 991–1006
DOI 10.4171/JST/319