4 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…
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…
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…