7 papers
The Essential Spectrum of the Linearized 2D Euler Operator is a Vertical Band
Roman Shvidkoy, Yuri Latushkin
We prove that the essential spectrum of the operator obtained by linearization about a steady state of the Euler equations governing the motion of inviscid ideal fluid in dimension…
Isospectral Theory of Euler Equations
Yanguang Charles Li, Roman Shvidkoy
Isospectral problem of both 2D and 3D Euler equations of inviscid fluids, is investigated. Connections with the Clay problem are described. Spectral theorem of the Lax pair is stud…
Counterexample to the Trotter product formula for projections
Mate Matolcsi, Roman Shvidkoy
We constructed a unitary semigroup on a Hilbert space and an orthogonal projection such that the limit does…
Hyperbolicity of semigroups and Fourier multipliers
Yuri Latushkin, Roman Shvidkoy
We present a characterization of hyperbolicity for strongly continuous semigroups on Banach spaces in terms of Fourier multiplier properties of the resolvent of the generator. Hype…
Narrow operators and rich subspaces of Banach spaces with the Daugavet property
Vladimir Kadets, Roman Shvidkoy, Dirk Werner
Let be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on which depend only on the norms of images of…
Some Remarks on Vector-Valued Integration
V Kadets, B. Shumyatskiy, R. Shvidkoy +2
The article presents a new method of integration of functions with values in Banach spaces. This integral and related notions prove to be a useful tool in the study of Banach space…