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Published in:
2015 | OriginalPaper | Chapter
Discrete Singular Integrals in a Half-Space
Authors : Alexander V. Vasilyev, Vladimir B. Vasilyev
Published in: Current Trends in Analysis and Its Applications
Publisher: Springer International Publishing
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Abstract
We consider Calderon–Zygmund singular integral in the discrete half-space \(h\mathbf{Z}^{m}_{+}\), where Z
m
is entire lattice (h>0) in R
m
, and prove, that the discrete singular integral operator is invertible in \(L_{2}(h\mathbf{Z}^{m}_{+})\) 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.