A discrete Hardy's Uncertainty Principle and discrete evolutions

TL;DR

This paper establishes a discrete analogue of Hardy's uncertainty principle using complex analysis, and interprets it through the decay properties of solutions to discrete Schrödinger and heat equations.

Contribution

It introduces a novel discrete version of Hardy's uncertainty principle and links it to the behavior of solutions in discrete quantum and thermal models.

Findings

Discrete Hardy's uncertainty principle proven using complex variable techniques

Interpretation of the principle in terms of decay of solutions to discrete Schrödinger and heat equations

Provides a new perspective on uncertainty principles in discrete settings

Abstract

In this paper we give a discrete version of Hardy's uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy's principle. Moreover, we give an interpretation of this principle in terms of decaying solutions to the discrete Schr\"odinger and heat equations.