arXiv subjects
Publications and source records attributed to Anastasia Mashinets.
We study a general discrete boundary value problem in Sobolev--Slobodetskii spaces in a plane quadrant and reduce it to a system of integral equations. We show a solvability of the system for a small size of discreteness starting from a solvability of its continuous analogue.
We consider discrete analogue of model pseudo-differential equations in discrete plane sector using discrete variant of Sobolev--Slobodetskii spaces. Starting from the concept of wave factorization for elliptic periodic symbol we describe solvability conditions for the equations and corresponding discrete boundary value problems. We give also a comparison between discrete and continuous solutions in appropriate discrete normed spaces.