On the absolutely continuous spectrum of generalized indefinite strings

Abstract

We 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 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 conservative Camassa-Holm flow in the dispersive regime is essentially supported on the interval $[1/4,\infty )$.

29 pages

References in corpus (4)

• On an integrable two-component Camassa-Holm shallow water system
• An isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation
• Poisson structure and Action-Angle variables for the Camassa-Holm equation
• A spectral Szego theorem on the real line

Cited by in corpus (5)

• Quantum graphs on radially symmetric antitrees
• De Branges canonical systems with finite logarithmic integral
• Trace formulas and inverse spectral theory for generalized indefinite strings
• Generalized indefinite strings with purely discrete spectrum
• On the absolutely continuous spectrum of generalized indefinite strings II