17 citations · 36 across the 11 of their papers we have counts for
11 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 the Daugavet property for ultraproducts
Dmitriy Bilik, Vladimir Kadets, Roman Shvidkoy +1
We show that if is a narrow operator on or , then the restrictions to and are narrow and conversely. We…
Narrow operators on vector-valued sup-normed spaces
Dmitriy Bilik, Vladimir Kadets, Roman Shvidkoy +2
We characterise narrow and strong Daugavet operators on -spaces; these are in a way the largest sensible classes of operators for which the norm equation $\|Id+T\| = 1+\|T\…