On a discrete boundary value problem in a quarter-plane

Abstract

We study a special discrete boundary value problem for a digital elliptic pseudodifferential operator in a discrete quadrant. Using a special periodic wave factorization for a symbol of the pseudo-differential operator we can construct a general solution of the pseudodifferential equation and then to choose appropriate boundary conditions for its unique solvability in corresponding Sobolev-Slobodetskii spaces. We also give a comparison between discrete and continuous solutions for boundary value problems under consideration