Uniqueness in weighted $l^p$ spaces for the Schr\"odinger equation on infinite graphs

TL;DR

This paper studies the uniqueness of solutions to Schr"odinger equations on infinite graphs within weighted ulul spaces, linking potential functions and weights to solution behavior.

Contribution

It introduces conditions for uniqueness of solutions in weighted ulul spaces on infinite graphs, extending previous results to more general settings.

Findings

Established criteria for solution uniqueness based on weights and potentials.

Extended the analysis of Schr"odinger equations to infinite graph structures.

Provided new insights into the role of weights in solution behavior.

Abstract

We investigate uniqueness of solutions to Schr\"odinger-type elliptic equations posed on infinite graphs. Solutions are assumed to belong to suitable weighted $\ell^p$ spaces where $p\geq 1$ and the weight is related to both the potential and $p$