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On the absolutely continuous spectrum of generalized indefinite strings II

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Abstract

We continue to investigate the 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 (−∞, −1/2] ⋃ [1/2, ∞).

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Acknowledgments

We thank Rossen Ivanov for helpful discussions and the anonymous reviewer for useful comments and hints with respect to the literature.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Loughborough University, Epinal Way, Loughborough, Leicestershire, LE11 3TU, UK

    Jonathan Eckhardt

  2. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria

    Jonathan Eckhardt & Aleksey Kostenko

  3. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, 1000, Ljubljana, Slovenia

    Aleksey Kostenko & Teo Kukuljan

Authors
  1. Jonathan Eckhardt
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  2. Aleksey Kostenko
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  3. Teo Kukuljan
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Correspondence to Jonathan Eckhardt.

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Research supported by the Austrian Science Fund (FWF) under Grants No. P29299 (J.E.) and P28807 (A.K.) as well as by the Slovenian Research Agency (ARRS) under Grant No. J1-9104 (A.K.)

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Eckhardt, J., Kostenko, A. & Kukuljan, T. On the absolutely continuous spectrum of generalized indefinite strings II. Isr. J. Math. 250, 307–344 (2022). https://doi.org/10.1007/s11856-022-2339-x

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  • DOI: https://doi.org/10.1007/s11856-022-2339-x

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