56 citations · 549 across the 34 of their papers we have counts for
26 papers · 1 filter
Trace formulas and inverse spectral theory for generalized indefinite strings
Jonathan Eckhardt, Aleksey Kostenko
Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and 2x2 canonica…
Generalized indefinite strings with purely discrete spectrum
Jonathan Eckhardt, Aleksey Kostenko
We establish criteria for the spectrum of a generalized indefinite string to be purely discrete and to satisfy Schatten-von Neumann properties. The results can be applied to the is…
Continued fraction expansions of Herglotz-Nevanlinna functions and generalized indefinite strings of Stieltjes type
Jonathan Eckhardt
We employ some results about continued fraction expansions of Herglotz-Nevanlinna functions to characterize the spectral data of generalized indefinite strings of Stieltjes type. I…
Trace formulas and continuous dependence of spectra for the periodic conservative Camassa-Holm flow
Jonathan Eckhardt, Aleksey Kostenko, Noema Nicolussi
This article is concerned with the isospectral problem \[ -f'' + \frac{1}{4} f = zωf + z^2 \upsilon f \] for the periodic conservative Camassa-Holm flow, where is a periodic re…
On the absolutely continuous spectrum of generalized indefinite strings II
Jonathan Eckhardt, Aleksey Kostenko, Teo Kukuljan
We continue to investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely…
On the absolutely continuous spectrum of generalized indefinite strings
Jonathan Eckhardt, Aleksey Kostenko
We investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous s…
The inverse spectral problem for periodic conservative multi-peakon solutions of the Camassa-Holm equation
Jonathan Eckhardt, Aleksey Kostenko
We solve the inverse spectral problem associated with periodic conservative multi-peakon solutions of the Camassa-Holm equation. The corresponding isospectral sets can be identifie…
The inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data
Jonathan Eckhardt
We establish the inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data. In particular, it is employed to prove existence of weak solutions fo…
Spectral asymptotics for canonical systems
Jonathan Eckhardt, Aleksey Kostenko, Gerald Teschl
Based on continuity properties of the de Branges correspondence, we develop a new approach to study the high-energy behavior of Weyl-Titchmarsh and spectral functions of …
On Spectral Deformations and Singular Weyl Functions for One-Dimensional Dirac Operators
Alexander Beigl, Jonathan Eckhardt, Aleksey Kostenko +1
We investigate the connection between singular Weyl-Titchmarsh-Kodaira theory and the double commutation method for one-dimensional Dirac operators. In particular, we compute the s…
The inverse spectral problem for indefinite strings
Jonathan Eckhardt, Aleksey Kostenko
Motivated by the study of certain nonlinear wave equations (in particular, the Camassa-Holm equation), we introduce a new class of generalized indefinite strings associated with di…
Quadratic operator pencils associated with the conservative Camassa-Holm flow
Jonathan Eckhardt, Aleksey Kostenko
We discuss direct and inverse spectral theory for a Sturm-Liouville type problem with a quadratic dependence on the eigenvalue parameter, which arises as the isospectral problem fo…
An isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation
Jonathan Eckhardt, Aleksey Kostenko
We introduce a generalized isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation. Utilizing the solution of the indefinite moment problem…
Inverse Spectral Problems for Schrödinger-Type Operators with Distributional Matrix-Valued Potentials
Jonathan Eckhardt, Fritz Gesztesy, Roger Nichols +2
The principal purpose of this note is to provide a reconstruction procedure for distributional matrix-valued potential coefficients of Schrödinger-type operators on a half-line fro…
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 -interaction on a subset of the real line of Lebesgue measure zero which is based on Sturm-Liouville differential expression with m…
Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators
Rainer Brunnhuber, Jonathan Eckhardt, Aleksey Kostenko +1
We develop singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators. In particular, we establish existence of a spectral transformation as well as local Borg-Mar…
An inverse spectral problem for a star graph of Krein strings
Jonathan Eckhardt
We solve an inverse spectral problem for a star graph of Krein strings, where the known spectral data comprises the spectrum associated with the whole graph, the spectra associated…
Inverse Spectral Theory for Sturm-Liouville Operators with Distributional Potentials
Jonathan Eckhardt, Fritz Gesztesy, Roger Nichols +1
We discuss inverse spectral theory for singular differential operators on arbitrary intervals associated with rather general differential expressions o…
Supersymmetry and Schrödinger-type operators with distributional matrix-valued potentials
Jonathan Eckhardt, Fritz Gesztesy, Roger Nichols +1
Building on work on Miura's transformation by Kappeler, Perry, Shubin, and Topalov, we develop a detailed spectral theoretic treatment of Schrödinger operators with matrix-valued p…
Singular Weyl-Titchmarsh-Kodaira Theory for Jacobi Operators
Jonathan Eckhardt, Gerald Teschl
We develop singular Weyl-Titchmarsh-Kodaira theory for Jacobi operators. In particular, we establish existence of a spectral transformation as well as local Borg-Marchenko and Hoch…
Two inverse spectral problems for a class of singular Krein strings
Jonathan Eckhardt
We solve the inverse problem from the spectral measure and the inverse three-spectra problem for the class of singular Krein strings on a finite interval with trace class resolvent…
Direct and inverse spectral theory of singular left-definite Sturm-Liouville operators
Jonathan Eckhardt
We discuss direct and inverse spectral theory of self-adjoint Sturm-Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop s…
Uniqueness Results for Schroedinger Operators on the Line with Purely Discrete Spectra
Jonathan Eckhardt, Gerald Teschl
We provide an abstract framework for singular one-dimensional Schroedinger operators with purely discrete spectra to show when the spectrum plus norming constants determine such an…
Inverse uniqueness results for Schrödinger operators using de Branges theory
Jonathan Eckhardt
We utilize the theory of de Branges spaces to show when certain Schrödinger operators with strongly singular potentials are uniquely determined by their associated spectral measure…