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On discrete pseudo-differential operators and equations

Vasilyev Vladimir (Belgorod State National Research University, Belgorod, Russia)

We introduce discrete pseudo-differential operators in appropriate discrete Sobolev-Slobodetskii spaces. Using discrete Fourier transform and factorization concept we study invertibility of such operators in some discrete spaces. Some examples for discrete Calderon-Zygmund operators and difference operators are considered.

Keywords: discrete operator, discrete Sobolev-Slobodetskii space, periodic wave factorization, periodic boundary value problem