On the solutions of generalized discrete Poisson equation

TL;DR

This paper investigates the generalized multidimensional discrete Poisson equation, establishing conditions for the existence and uniqueness of solutions with square-summable derivatives using Fourier analysis.

Contribution

It introduces a framework for solving the generalized discrete Poisson equation and proves uniqueness and existence conditions using Fourier transform techniques.

Findings

Solutions with square-summable derivatives are unique up to a constant.

Provides a necessary condition for the existence of solutions.

Uses Fourier transform as the main analytical tool.

Abstract

The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with square-summable discrete derivatives are unique up to a constant. The proof uses the Fourier transform as the main tool. The necessary condition for the existence of the solution is provided.