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Download fileThe inverse spectral problem for indefinite strings
journal contribution
posted on 2018-10-04, 10:38 authored by Jonathan EckhardtJonathan Eckhardt, Aleksey KostenkoMotivated 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 differential equations of the form
−u" = z u ω + z2u υ on an interval [0, L), where ω is a real-valued distribution in H
−1loc [0, L), υ is a non-negative Borel measure on [0, L) and z is a complex spectral parameter. Apart from developing basic spectral theory for these kinds of spectral problems, our main result is an indefinite analogue of M. G. Krein’s celebrated solution of the inverse spectral problem for inhomogeneous vibrating strings.
Funding
Research supported by the Austrian Science Fund (FWF) under Grants No. J3455 and P26060.
History
School
- Science
Department
- Mathematical Sciences
Published in
Inventiones mathematicaeVolume
204Issue
3Pages
939 - 977Citation
ECKHARDT, J. and KOSTENKO, A., 2016. The inverse spectral problem for indefinite strings. Inventiones mathematicae, 204(3), pp. 939-977.Publisher
© SpringerVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2015-09-27Publication date
2015-10-13Notes
This is a post-peer-review, pre-copyedit version of an article published in Inventiones mathematicae. The final authenticated version is available online at: https://doi.org/10.1007/s00222-015-0629-1ISSN
0020-9910eISSN
1432-1297Publisher version
Language
- en