5 citations · 7 across the 10 of their papers we have counts for
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On a general discrete boundary value problem
Vladimir Vasilyev, Alexander Vasilyev, Anastasia Mashinets
We study a general discrete boundary value problem in Sobolev--Slobodetskii spaces in a plane quadrant and reduce it to a system of integral equations. We show a solvability of the…
On discrete boundary value problems with nonlocal conditions in a quarter-plane
Vladimir Vasilyev, Anastasia Mashinets
We consider discrete analogue of model pseudo-differential equations in discrete plane sector using discrete variant of Sobolev--Slobodetskii spaces. Starting from the concept of w…
On some solvability theorems for pseudo-differential equations
Vladimir Vasilyev, Victor Polunin, Igor Shmal
We study a model elliptic pseudo-differential equation and simplest boundary value problems for a half-space and a special cone in Sobolev--Slobodetskii spaces which have different…
On asymptotical expansions for certain singular integrals: 2-dimensional case
Vladimir B. Vasilyev
One discusses a problem of asymptotical behavior for some operators in a general theory of pseudo differential equations on manifolds with borders. Using the distribution theory on…
The factorization technique for difference equations
Alexander Vasilyev, Vladimir Vasilyev
We study multidimensional difference equations with a continual variable in the Sobolev--Slobodetskii spaces. Using ideas and methods of the theory of boundary value problems for e…
Discrete singular integrals in a half-space
Alexander V. Vasilyev, Vladimir B. Vasilyev
We consider Calderon -- Zygmund singular integral in the discrete half-space , where is entire lattice () in , and prove that the discre…
Potentials for elliptic boundary value problems in cones
Vladimir Vasilyev
We consider an elliptic pseudo differential equation in a multi-dimensional cone and starting wave factorization concept we add some boundary conditions. For the simplest cases exp…