30 citations · 128 across the 34 of their papers we have counts for
7 papers · 1 filter
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…
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…
An extended Hilbert scale and its applications
Vladimir Mikhailets, Aleksandr Murach, Tetiana Zinchenko
We propose a new viewpoint on Hilbert scales extending them by means of all Hilbert spaces that are interpolation ones between spaces on the scale. We prove that this extension adm…
Hörmander spaces on manifolds, and their application to elliptic boundary-value problems
T. M. Kasirenko, A. A. Murach, I. S. Chepurukhina
We introduce an extended Sobolev scale on a smooth compact manifold with boundary. The scale is formed by inner-product Hörmander spaces for which an RO-varying radial function ser…
The Refined Sobolev Scale, Interpolation, and Elliptic Problems
Vladimir A. Mikhailets, Aleksandr A. Murach
The paper gives a detailed survey of recent results on elliptic problems in Hilbert spaces of generalized smoothness. The latter are the isotropic Hörmander spaces $H^{s,φ}:=B_{2,μ…
General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series
Vladimir A. Mikhailets, Aleksandr A. Murach
We prove that the classical Menshov-Rademacher, Orlicz, and Tandori theorems remain true for orthogonal series given in the direct integrals of measurable collections of Hilbert sp…