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arXiv · 1807.09491

Ground States for Nonlocal Schr\"odinger Type Operators on Locally Compact Abelian Groups

Anatoly N. Kochubei·Yuri Kondratiev
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Abstract

We find classes of nonlocal operators of Schr\"odinger 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.

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Anatoly N. Kochubei, Yuri Kondratiev. 2018-07-25. Ground States for Nonlocal Schr\"odinger Type Operators on Locally Compact Abelian Groups. https://arxiv.org/abs/1807.09491

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