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math.SP2025
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…
math.SP2024
First-order asymptotic perturbation theory for extensions of symmetric operators
Yuri Latushkin, Selim Sukhtaiev
This work offers a new prospective on asymptotic perturbation theory for varying self-adjoint extensions of symmetric operators. Employing symplectic formulation of self-adjointnes…
math.SP2024
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…