Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 289–296 | Cite as

Discrete Pseudo-Differential Operators and Boundary Value Problems in a Half-Space and a Cone

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Abstract

We consider a certain class of discrete pseudo-differential operators and related equations in a sharp convex cone and describe their invertibility conditions in L2 spaces. For this purpose we introduce a concept of periodic wave factorization for elliptic symbol and show its applicability for the studying. For a half-space case we consider the Laplace equation and describe a solution of the discrete Dirichlet problem.

Keywords and phrases

Discrete operator multidimensional periodic Riemann problem periodic wave factorization invertibility discrete boundary condition 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Chair of Differential EquationsBelgorod National Research UniversityBelgorodRussia

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