48 citations · 95 across the 17 of their papers we have counts for
20 papers
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 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,…
Well-posedness of Keller-Segel systems on compact metric graphs
Hewan Shemtaga, Wenxian Shen, Selim Sukhtaiev
Chemotaxis phenomena govern the directed movement of micro-organisms in response to chemical stimuli. In this paper, we investigate two Keller--Segel systems of reaction-advection-…
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…
Stability and bifurcation for logistic Keller--Segel models on compact graphs
Hewan Shemtaga, Wenxian Shen, Selim Sukhtaiev
This paper concerns asymptotic stability, instability, and bifurcation of constant steady state solutions of the parabolic-parabolic and parabolic-elliptic chemotaxis models on met…
Spectral properties of Schrödinger operators with locally potentials
Milivoje Lukić, Selim Sukhtaiev, Xingya Wang
We study half-line Schrödinger operators with locally potentials. In the first part, we focus on a general spectral theoretic framework for such operators, including a Las…
Resolvent expansions for self-adjoint operators via boundary triplets
Yuri Latushkin, Selim Sukhtaiev
In this paper we develop certain aspects of perturbation theory for self-adjoint operators subject to small variations of their domains. We use the abstract theory of boundary trip…
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…
Random Hamiltonians with Arbitrary Point Interactions
David Damanik, Jake Fillman, Mark Helman +2
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real l…
Zero Measure and Singular Continuous Spectra for Quantum Graphs
David Damanik, Licheng Fang, Selim Sukhtaiev
We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a nontrivial sin…
Localization for Anderson Models on Metric and Discrete Tree Graphs
David Damanik, Jake Fillman, Selim Sukhtaiev
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contain…
An index theorem for Schrödinger operators on metric graphs
Yuri Latushkin, Selim Sukhtaiev
We show that the spectral flow of a one-parameter family of Schrödinger operators on a metric graph is equal to the Maslov index of a path of Lagrangian subspaces describing the ve…
Limits of Quantum Graph Operators With Shrinking Edges
Gregory Berkolaiko, Yuri Latushkin, Selim Sukhtaiev
We address the question of convergence of Schrödinger operators on metric graphs with general self-adjoint vertex conditions as lengths of some of graph's edges shrink to zero. We…
Anderson Localization for Radial Tree Graphs With Random Branching Numbers
David Damanik, Selim Sukhtaiev
We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operato…
The Maslov Index and the Spectra of Second Order Elliptic Operators
Yuri Latushkin, Selim Sukhtaiev
We consider second order elliptic differential operators on a bounded Lipschitz domain . Firstly, we establish a natural one-to-one correspondence between their self-adjoint ext…
A bound for the eigenvalue counting function for Krein--von Neumann and Friedrichs extensions
Mark S. Ashbaugh, Fritz Gesztesy, Ari Laptev +2
For an arbitrary open, nonempty, bounded set , , and sufficiently smooth coefficients , we consider the closed, strictly positive, h…
Counting spectrum via the Maslov index for one dimensional periodic Schrödinger operators
Christopher K. R. T. Jones, Yuri Latushkin, Selim Sukhtaiev
We study the spectrum of the Schrödinger operators with matrix valued potentials on a finite interval subject to periodic boundary conditions. For two such operator…
The Morse and Maslov Indices for Schrödinger Operators
Yuri Latushkin, Alim Sukhtayev, Selim Sukhtaiev
We study the spectrum of Schrödinger operators with matrix valued potentials utilizing tools from infinite dimensional symplectic geometry. Using the spaces of abstract boundary va…
A Bound for the Eigenvalue Counting Function for Higher-Order Krein Laplacians on Open Sets
Fritz Gesztesy, Ari Laptev, Marius Mitrea +1
For an arbitrary nonempty, open set , , of finite (Euclidean) volume, we consider the minimally defined higher-order Laplacian $(- Δ)^m\big…