IndefiniteString.pdf (412.74 kB)
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