33 citations · 63 across the 6 of their papers we have counts for
6 papers
Elliptic problems and Hörmander spaces
Vladimir A. Mikhailets, Aleksandr A. Murach
The paper gives a survey of the modern results on elliptic problems on the Hörmander function spaces. More precisely, elliptic problems are studied on a Hilbert scale of the isotro…
Spectral gaps of the one-dimensional Schrödinger operators with singular periodic potentials
Vladimir Mikhailets, Volodymyr Molyboga
The behaviour of the lengths of spectral gaps of the Hill-Schrödinger operators S(q)u=-u''+q(x)u,\quad u\in \mathrm{Dom}(S(q)) with real-valued 1-peri…
Regular elliptic boundary-value problem in a two-sided refined scale of spaces
Vladimir A. Mikhailets, Aleksandr A. Murach
A regular elliptic boundary-value problem over a bounded domain with a smooth boundary is studied. We prove that the operator of this problem is a Fredholm one in the two-sided ref…
Interpolation with a function parameter and refined scale of spaces
Vladimir A. Mikhailets, Alexandr A. Murach
The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the…
Elliptic systems of pseudodifferential equations in a refined scale on a closed manifold
Vladimir A. Mikhailets, Alexandr A. Murach
We study a system of pseudodifferential equations that is elliptic in the sense of Petrovskii on a closed compact smooth manifold. We prove that the operator generated by the syste…
Singularly perturbed periodic and semiperiodic differential operators
V. A. Mikhailets, V. M. Molyboga
Qualitative and spectral properties of the form-sums S_{\pm}(V):=D_{\pm}^{2m}\dotplus V(x),\quad m\in \mathbb{N}, in the Hilbert space are studied. Here the periodic $…