Dmitry Chelkak

activity

20052021

most citedRevisiting the combinatorics of the 2D Ising model

45 citations · 242 across the 24 of their papers we have counts for

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5 papers · 1 filter

math.SP2009

An application of the fixed point theorem to the inverse Sturm-Liouville problem

Dmitry Chelkak

We consider Sturm-Liouville operators $- y^{''} + v (x) y$ on $[0, 1]$ with Dirichlet boundary conditions $y (0) = y (1) = 0$ . For any $1 \leq p < \infty$ , we give a short proof of the characterizati…

math.SP2008★ 5 cited

Weyl-Titchmarsh functions of vector-valued Sturm-Liouville operators on the unit interval

Dmitry Chelkak, Evgeny Korotyaev

The matrix-valued Weyl-Titchmarsh functions $M (λ)$ of vector-valued Sturm-Liouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collec…

math.SP2006★ 26 cited

The inverse problem for perturbed harmonic oscillator on the half-line with Dirichlet boundary conditions

Dmitry Chelkak, Evgeny Korotyaev

We consider the perturbed harmonic oscillator $T_{D} ψ = - ψ^{''} + x^{2} ψ + q (x) ψ$ , $ψ (0) = 0$ , in $L^{2} (R_{+})$ , where $q\in\bH_+=\{q', xq\in L^2(\R_+)\}$ is a real-valued potential. We prove that…

math.SP2006

Parametrization of the isospectral set for the vector-valued Sturm-Liouville problem

Dmitry Chelkak, Evgeny Korotyaev

We obtain a parametrization of the isospectral set of matrix-valued potentials for the vector-valued Sturm-Liouville problem on a finite interval.

math.SP2006★ 4 cited

Inverse spectral analysis for finite matrix-valued Jacobi operators

Jochen Brüning, Dmitry Chelkak, Evgeny Korotyaev

Consider the Jacobi operators $\cJ$ given by $(\cJ y)_n=a_ny_{n+1}+b_ny_n+a_{n-1}^*y_{n-1}$, $y_n\in \C^m$ (here $y_{0} = y_{p + 1} = 0$ ), where $b_{n} = b_{n}^{*}$ and $a_{n} : det a_{n} \neq = 0$ are the…