Inverse scattering problem for a special class of canonical systems and non-linear fourier integral. part I: Asymptotics of eigenfunctions

S. Kupin, F. Peherstorfer, A. Volberg, P. Yuditskii

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

An original approach to the inverse scattering for Jacobi matrices was recently suggested in [20]. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however they did not take into account the mass point spectrum. This paper follows similar lines for the continuous setting with an absolutely continuous spectrum on the half-axis and a pure point spectrum on the negative half-axis satisfying the Blaschke condition. This leads us to the solution of the inverse scattering problem for a class of canonical systems that generalizes the case of Sturm-Liouville (Schrödinger) operator.

Original languageEnglish
Title of host publicationMethods of Spectral Analysis in Mathematical Physics - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2006
EditorsSergei Naboko, Ari Laptev, Jan Janas, Ari Laptev, Gunter Stolz, Pavel Kurasov
PublisherSpringer International Publishing
Pages285-323
Number of pages39
ISBN (Print)9783764387549
StatePublished - 2009
EventConference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2006 - Lund, Sweden
Duration: 1 Jan 2006 → …

Publication series

NameOperator Theory: Advances and Applications
Volume186
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Conference

ConferenceConference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2006
Country/TerritorySweden
CityLund
Period1/01/06 → …

Bibliographical note

Publisher Copyright:
© 2008 Birkhäuser Verlag Basel/Switzerland.

Funding

FundersFunder number
Directorate for Mathematical and Physical Sciences0501067, 0200713

    Keywords

    • Asymptotical behavior of the solutions
    • Canonical system
    • Inverse scattering problem
    • Model space
    • Reproducing kernels
    • Schrödinger operator

    Fingerprint

    Dive into the research topics of 'Inverse scattering problem for a special class of canonical systems and non-linear fourier integral. part I: Asymptotics of eigenfunctions'. Together they form a unique fingerprint.

    Cite this