Discrete Pseudo-Differential Operators and Boundary Value Problems in a Half-Space and a Cone
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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 phrasesDiscrete operator multidimensional periodic Riemann problem periodic wave factorization invertibility discrete boundary condition
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- 8.V. S. Vladimirov, Methods of the Theory of Functions of Many Complex Variables (Dover, New York, 2007).Google Scholar