%0 Journal Article
%T Discrete singular integrals in a half-space
%A Alexander V. Vasilyev
%A Vladimir B. Vasilyev
%J Mathematics
%D 2014
%I arXiv
%X We consider Calderon -- Zygmund singular integral in the discrete half-space $h{\bf Z}^m_{+}$, where ${\bf Z}^m$ is entire lattice ($h>0$) in ${\bf R}^m$, and prove that the discrete singular integral operator is invertible in $L_2(h{\bf Z}^m_{+}$) iff such is its continual analogue. The key point for this consideration takes solvability theory of so-called periodic Riemann boundary problem, which is constructed by authors.
%U http://arxiv.org/abs/1410.1049v1