Institute of Applied Mathematics and Mechanics

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19962026

most citedLong-Time Asymptotics for the Camassa-Holm Equation

227 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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16 papers · 1 filter

math.SP2020★ 4 cited

Non-compact quantum graphs with summable matrix potentials

Yaroslav Granovskyi, Mark Malamud, Hagen Neidhardt

Let $G$ be a metric noncompact connected graph with finitely many edges. The main object of the paper is the Hamiltonian $H_{α}$ associated in $L^2(\mathcal{G};\mathb…

math.SP2016★ 9 cited

Schrödinger Operators with $δ$ -interactions in a Space of Vector-Valued Functions

Aleksey Kostenko, Mark Malamud, Daria Natiagailo

We study spectral properties of Schrödinger operators with $δ$ -interactions on a semi-axis by using the theory of boundary triplets and the corresponding Weyl functions. We establi…

math.SP2014★ 20 cited

One-dimensional Schroedinger operators with delta-prime-interactions on Cantor-type sets

Jonathan Eckhardt, Aleksey Kostenko, Mark Malamud +1

We introduce a novel approach for defining a $δ^{'}$ -interaction on a subset of the real line of Lebesgue measure zero which is based on Sturm-Liouville differential expression with m…

math.SP2013★ 2 cited

On the spectrum of the operator which is a composition of integration and substitution

Ignat Domanov

We study the spectrum of the Volterra composition operator in the space $L_{2} [0, 1]$

math.SP2013

On the spectrum and eigenfunctions of the operator $(V f) (x) = \int_{0}^{x^{α}} f (t) d t$

Ignat Domanov

We find spectrum and eigenfunctions of the operator $(V f) (x) = \int_{0}^{x^{α}} f (t) d t$ in $L_{2} [0, 1]$

math.SP2012★ 3 cited

Optimization of quasi-normal eigenvalues for Krein-Nudelman strings

Illya M. Karabash

The paper is devoted to optimization of resonances for Krein strings with total mass and statical moment constraints. The problem is to design for a given $α \in R$ a string that h…

math.SP2010★ 40 cited

Commutation Methods for Schroedinger Operators with Strongly Singular Potentials

Aleksey Kostenko, Alexander Sakhnovich, Gerald Teschl

We explore the connections between singular Weyl-Titchmarsh theory and the single and double commutation methods. In particular, we compute the singular Weyl function of the commut…

math.SP2010★ 61 cited

On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schroedinger Operators

Aleksey Kostenko, Gerald Teschl

We investigate the singular Weyl-Titchmarsh m-function of perturbed spherical Schroedinger operators (also known as Bessel operators) under the assumption that the perturbation $q(…

math.SP2010★ 64 cited

Weyl-Titchmarsh Theory for Schroedinger Operators with Strongly Singular Potentials

Aleksey Kostenko, Alexander Sakhnovich, Gerald Teschl

We develop Weyl-Titchmarsh theory for Schroedinger operators with strongly singular potentials such as perturbed spherical Schroedinger operators (also known as Bessel operators).…

math.SP2009

On the Spectral Analysis of Direct Sums of Riemann-Liouville Operators in Sobolev Spaces of Vector Functions

I. Yu. Domanov, M. M. Malamud

Let $J_{k}^{α}$ be a real power of the integration operator $J_{k}$ defined on Sobolev space $W_{p}^{k} [0, 1]$ . We investigate the spectral properties of the operator $A_k=\bigoplus_{j=1}^n λ…

math.SP2009★ 5 cited

A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators

I. M. Karabash

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach t…

math.SP2008

Generalized Jacobi operators in Krein spaces

Maxim Derevyagin

A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of t…

math.SP2008★ 48 cited

The similarity problem for $J$ -nonnegative Sturm-Liouville operators

Illya M. Karabash, Aleksey S. Kostenko, Mark M. Malamud

Sufficient conditions for the similarity of the operator $A := 1/ r (x) (- d^{2} / d x^{2} + q (x))$ with an indefinite weight $r(x)=(\sgn x)|r(x)|$ are obtained. These conditions are formulat…

math.SP2007★ 16 cited

Abstract kinetic equations with positive collision operators

I. M. Karabash

We consider "forward-backward" parabolic equations in the abstract form $J d ψ / d x + L ψ = 0$ , $0 < x < τ \leq \infty$ , where $J$ and $L$ are operators in a Hilbert space $H$ such th…

math.SP2007★ 26 cited

Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn x

I. Karabash, C. Trunk

We consider a singular Sturm-Liouville expression with the indefinite weight sgn x. To this expression there is naturally a self-adjoint operator in some Krein space associated. We…

math.SP2006★ 17 cited

Indefinite Sturm-Liouville operators with the singular critical point zero

Illya M. Karabash, Aleksey S. Kostenko

We present a new necessary condition for similarity of indefinite Sturm-Liouville operators to self-adjoint operators. This condition is formulated in terms of Weyl-Titchmarsh $m$ -…