On the Uniqueness of the Finite-Difference Analogues of the Fundamental Solution of the Heat Equation and the Wave Equation in Discrete Potential Theory

The paper considers the problem of uniquely determining the fundamental solution of the finite-difference analogs of the wave equation and the heat equation in the framework of the discrete potential theory. Finite-difference fundamental solutions of finite-difference analogues of partial differential equations make it possible to solve direct and inverse problems of reconstructing wave and heat sources in various media from heterogeneous and multi-current information about the corresponding physical fields. The article considers formulations with Dirichlet conditions in three- and four-dimensional Cartesian spaces.