One considers a general difference equation in a multidimensional space with continuous coefficients in the space of integrable functions. Necessary and sufficient conditions for a Fredholm property are obtained with a help of the Fourier transform and the Riemann boundary value problem. For simplest cases solvability conditions and formula of a general solution for the difference equation are given.
Vasilyev, A. V., & Vasilyev, V. B. (2016). Difference Equations in a Multidimensional Space. Mathematical Modelling and Analysis, 21(3), 336-349. https://doi.org/10.3846/13926292.2016.1161668
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