5 papers · 1 filter
The calculus of Duistermaat's triple index
Gregory Berkolaiko, Graham Cox, Yuri Latushkin +1
In this paper we develop a systematic calculus for the Duistermaat index, a symplectic invariant defined for triples of Lagrangian subspaces. Introduced nearly half a century ago,…
Hadamard-type formulas for real eigenvalues of canonically symplectic operators
Mitchell Curran, Selim Sukhtaiev
We give first-order asymptotic expansions for the resolvent and Hadamard-type formulas for the eigenvalue curves of one-parameter families of canonically symplectic operators. We a…
Some Remarks On Krein--von Neumann Extensions
Fritz Gesztesy, Selim Sukhtaiev
We survey various properties of Krein--von Neumann extensions and the reduced Krein--von Neumann operator $\hatt S_K$ in connection with a strictly positive (symmetric) opera…
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…
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…