On some approximate calculations for certain pseudo-di˙erential equations

Abstract

We consider discrete pseudo-di˙erential operatots and equations as approximate operators and equations for their continuous analogues. For this purpose we study a solvability for such equations in appropriate discrete spaces and give some error estimates for discrete and continuous solutions. This approach is based on the discrete Fourier transform and factorization tecnique which is used for special canonical domains in Euclidean space.