Ground states for nonlocal Schrödinger type operators on locally compact abelian groups

  • Anatoly N. Kochubei

    National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • Yuri Kondratiev

    Universität Bielefeld, Germany
Ground states for nonlocal Schrödinger type operators on locally compact abelian groups cover

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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