64 citations · 219 across the 45 of their papers we have counts for
47 papers
The Damped Waves Equation and generalized Cosine and Sine families on Banach spaces
Yuri Latushkin, Alin Pogan
We study the abstract damped wave equation on a Banach space, allowing the damping coefficient to be unbounded. By recasting the equation as a first-order system and identifying co…
Solutions of abstract wave equations, eigenvalues and resonances
Yuri Latushkin, Alin Pogan
We prove general representation formulas for strongly continuous cosine and sine operator families in terms of scattering resonances of their generators. This generalizes known res…
Resonances for the one dimensional Schrödinger operator with the matrix-valued complex square-well potential
Yuri Latushkin, Alin Pogan
We study the resonances of (generally, non-selfadjoint) Schrödinger operators with matrix-valued square-well potentials. We compute explicitly the Jost function and derive complex…
Characteristic determinants for a second order difference equation on the half-line arising in hydrodynamics
Yuri Latushkin, Shibi Vasudevan
We study the point spectrum of a second order difference operator with complex potential on the half-line via Fredholm determinants of the corresponding Birman-Schwinger operator p…
The Duistermaat index and eigenvalue interlacing for self-adjoint extensions of a symmetric operator
Gregory Berkolaiko, Graham Cox, Yuri Latushkin +1
Eigenvalue interlacing is a useful tool in linear algebra and spectral analysis. In its simplest form, the interlacing inequality states that a rank-one positive perturbation shift…
Uniform bounds of families of analytic semigroups and Lyapunov linear stability of planar fronts
Yuri Latushkin, Alin Pogan
We study families of analytic semigroups, acting in a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parame…