We introduce a digital pseudo-differential operator acting in discrete Sobolev--Slobodetskii spaces and consider pseudo-differential equations with such operators in a discrete half-space. The theorem on a general solution of such equations is proved for a special case.
We consider Calderon -Zygmund singular integral in the discrete half-space hZ 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 (hZ 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.MSC2010: 42A50, 42A85
We consider a model elliptic pseudodifferential equation in a special canonical domains of a multidimensional space. Using a special representation for an elliptic symbol, we give the formula for a general solution of such an equation and choose additional conditions under which this boundary value problem has a unique solution in appropriate Sobolev-Slobodetskii spaces. Also, we introduce some transmutation operators that help us in constructing the solution.
The paper is devoted to studying limit behavior for a solution of model elliptic pseudodifferential equation with some integral boundary condition in 4-wedge conical canonical 3D singular domain with two parameters. It is shown that the solution of such boundary value problem can have a limit with respect to endpoint values of the parameters in appropriate Sobolev-Slobodetskii space if the boundary function is a solution of a special functional singular integral equation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.