A Rellich Type Theorem for Discrete Schr{\"o}dinger Operators

TL;DR

This paper proves a discrete analogue of Rellich's theorem for the square lattice Laplacian, demonstrating unique continuation and ruling out embedded eigenvalues for discrete Schrödinger operators.

Contribution

It introduces a Rellich type theorem for discrete Laplacians and applies it to establish unique continuation and absence of embedded eigenvalues.

Findings

Proved a Rellich type theorem for discrete Laplacian.

Established unique continuation properties for certain domains.

Showed non-existence of embedded eigenvalues in discrete Schrödinger operators.

Abstract

An analogue of Rellich's theorem is proved for discrete Laplacian on square lattice, and applied to show unique continuation property on certain domains as well as non-existence of embedded eigenvalues for discrete Schr{\"o}dinger operators.