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On the ground state of lattice Schr\"{o}dinger operators by Jex, Michal; Štampach, František is a scholarly article available to read on EtoBox.

What is On the ground state of lattice Schr\"{o}dinger operators about?

We prove necessary and sufficient conditions for lattice Schr\"{o}dinger operators to have a zero energy bound state in arbitrary dimension. The two criteria are sharp, complementary, and depend crucially on both the dimension and asymptotic behaviour of the potential. The method relies on a discrete variant of Agmon's comparison principle which is also proven. Our results represent a discrete variant of the recent criteria obtained in the continuous setting by D. Hundertmark, M. Jex, and M. Lange [$\textit{Forum Mathematics, Sigma}$ $\textbf{11}$ (2023)].

Author

Jex, Michal; Štampach, František

Published

2023

Language

EN