Difference Equations in a Multidimensional Space - Vasilyev, Alexander V.; Vasilyev, Vladimir B. (Mathematical Modelling and Analysis, 2016)
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.