30 citations · 128 across the 34 of their papers we have counts for
39 papers
Matrix parabolic problems in Sobolev spaces of generalized smoothness
Valerii Los, Vladimir Mikhailets, Aleksandr Murach
We study a general linear parabolic problem for Petrovskii parabolic differential system in Sobolev anisotropic distribution spaces of generalized smoothness. Slowly varying functi…
Elliptic boundary-value problems in some distribution spaces of generalized smoothness
Anna Anop, Aleksandr Murach
We build a solvability theory of elliptic boundary-value problems in normed Sobolev spaces of generalized smoothness for any integrability exponent . The smoothness is given b…
Distribution spaces associated with elliptic operators
Iryna Chepurukhina, Aleksandr Murach
We study complex distribution spaces given over a bounded Lipschitz domain and associated with an elliptic differential operator with -coefficients on $\overlin…
Extended Sobolev scale for vector bundles, and its applications
Aleksandr Murach, Tetiana Zinchenko
We study an extended Sobolev scale for smooth vector bundles over a smooth closed manifold. This scale is built on the base of inner product distribution spaces of generalized smoo…
Unconditional convergence of eigenfunction expansions for abstract and elliptic operators
Vladimir Mikhailets, Aleksandr Murach
We study the most general class of eigenfunction expansions for abstract normal operators with pure point spectrum in a complex Hilbert space. We find sufficient conditions for suc…
A new look at old theorems of Fejér and Hardy
Vladimir Mikhailets, Aleksandr Murach, Oksana Tsyhanok
The article studies the convergence of trigonometric Fourier series via a new Tauberian theorem for Cesàro summable series in abstract normed spaces. This theorem generalizes some…