Selim Sukhtaiev
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View article: Some Remarks On Krein--von Neumann Extensions
Some Remarks On Krein--von Neumann Extensions Open
We survey various properties of Krein--von Neumann extensions $S_K$ and the reduced Krein--von Neumann operator $\hatt S_K$ in connection with a strictly positive (symmetric) operator $S$ with nonzero deficiency indices. In particular, we …
View article: The calculus of Duistermaat's triple index
The calculus of Duistermaat's triple index Open
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, this index has lately been the subject of renewed attention…
View article: Well-posedness of Keller–Segel systems on compact metric graphs
Well-posedness of Keller–Segel systems on compact metric graphs Open
Chemotaxis phenomena govern the directed movement of microorganisms in response to chemical stimuli. In this paper, we investigate two Keller–Segel systems of reaction–advection–diffusion equations modeling chemotaxis on thin networks. The…
View article: First‐order asymptotic perturbation theory for extensions of symmetric operators
First‐order asymptotic perturbation theory for extensions of symmetric operators Open
This work offers a new prospective on asymptotic perturbation theory for varying self‐adjoint extensions of symmetric operators. Employing symplectic formulation of self‐adjointness, we use a version of resolvent difference identity for tw…
View article: Spectral properties of Schrödinger operators with locally $H^{-1}$ potentials
Spectral properties of Schrödinger operators with locally $H^{-1}$ potentials Open
We study half-line Schrödinger operators with locally H^{-1} potentials. In the first part, we focus on a general spectral theoretic framework for such operators, including a Last–Simon-type description of the absolutely continuous spectru…
View article: Well-posedness of Keller-Segel systems on compact metric graphs
Well-posedness of Keller-Segel systems on compact metric graphs Open
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-diffusion equations modeling chemotaxis on thin networks. T…
View article: The Duistermaat index and eigenvalue interlacing for self-adjoint extensions of a symmetric operator
The Duistermaat index and eigenvalue interlacing for self-adjoint extensions of a symmetric operator Open
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 shifts each eigenvalue up, but not further than the next unpertu…
View article: Stability and bifurcation for logistic Keller--Segel models on compact graphs
Stability and bifurcation for logistic Keller--Segel models on compact graphs Open
This paper concerns asymptotic stability, instability, and bifurcation of constant steady state solutions of the parabolic-parabolic and parabolic-elliptic chemotaxis models on metric graphs. We determine a threshold value $χ^*>0$ of the c…
View article: Spectral properties of Schrödinger operators with locally $H^{-1}$ potentials
Spectral properties of Schrödinger operators with locally $H^{-1}$ potentials Open
We study half-line Schrödinger operators with locally $H^{-1}$ potentials. In the first part, we focus on a general spectral theoretic framework for such operators, including a Last--Simon-type description of the absolutely continuous spec…
View article: Resolvent expansions for self-adjoint operators via boundary triplets
Resolvent expansions for self-adjoint operators via boundary triplets Open
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 triplets to quantify such perturbations and give the second ord…
View article: First-order asymptotic perturbation theory for extensions of symmetric operators
First-order asymptotic perturbation theory for extensions of symmetric operators Open
This work offers a new prospective on asymptotic perturbation theory for varying self-adjoint extensions of symmetric operators. Employing symplectic formulation of self-adjointness we obtain a new version of Krein formula for resolvent di…
View article: Random Hamiltonians with Arbitrary Point Interactions
Random Hamiltonians with Arbitrary Point Interactions Open
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 line. Under minimal assumptions on the type of disorder, we …
View article: An index theorem for Schrödinger operators on metric graphs
An index theorem for Schrödinger operators on metric graphs Open
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 vertex conditions. In addition, we derive an Hadamard-type fo…
View article: Topics in spectral theory of differential operators
Topics in spectral theory of differential operators Open
This dissertation is devoted to two eigenvalue counting problems: Determining the asymptotic behavior of large eigenvalues of self-adjoint extensions of partial differential operators, and computing the number of negative eigenvalues for b…
View article: A bound for the eigenvalue counting function for Krein--von Neumann and\n Friedrichs extensions
A bound for the eigenvalue counting function for Krein--von Neumann and\n Friedrichs extensions Open
For an arbitrary open, nonempty, bounded set $\\Omega \\subset \\mathbb{R}^n$,\n$n \\in \\mathbb{N}$, and sufficiently smooth coefficients $a,b,q$, we consider\nthe closed, strictly positive, higher-order differential operator $A_{\\Omega,…