POSITIVITY OF A ONE-DIMENSIONAL DIFFERENCE OPERATOR IN THE HALF-LINE AND ITS APPLICATIONS

In the present paper, the positivity of one-dimensional difference operator in the half-line is considered. The structure of fractional spaces generated by difference operators in the half-line is investigated. The equivalence of the norms of these fractional spaces and Holder spaces is established. We also discuss its applications to partial differential equations and theory of difference schemes for partial differential equations.