56 citations · 549 across the 34 of their papers we have counts for
7 papers · 1 filter
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…