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# On the absolutely continuous spectrum of generalized indefinite strings II

journal contribution
posted on 19.04.2021, 12:34 by Jonathan EckhardtJonathan 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 continuous spectra of two more model examples of generalized indefinite strings under rather wide perturbations. In particular, one of these results allows us to prove that the absolutely continuous spectrum of the isospectral problem associated with the two-component Camassa-Holm system in a certain dispersive regime is essentially supported on the set $(-\infty,-1/2]\cup [1/2,\infty)$.

• Science

## Department

• Mathematical Sciences

## Published in

Israel Journal of Mathematics

Springer

## Version

AM (Accepted Manuscript)

## Publisher statement

This is a post-peer-review, pre-copyedit version of an article published in Israel Journal of Mathematics. The final authenticated version is available online at: http://dx.doi.org/[insert DOI]

27 pages

0021-2172

1565-8511

en

## Depositor

Dr Jonathan Eckhardt. Deposit date: 16 April 2021

## Exports

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