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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2311.01189 |
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| _version_ | 1866908089374998528 |
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| author | Eckhardt, Jonathan Kostenko, Aleksey |
| author_facet | Eckhardt, Jonathan Kostenko, Aleksey |
| contents | Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and 2x2 canonical systems). We prove a number of Szegő-type theorems for generalized indefinite strings and related spectral problems (including Krein strings, canonical systems and Dirac operators). More specifically, for several classes of coefficients (that can be regarded as Hilbert-Schmidt perturbations of model problems), we provide a complete characterization of the corresponding set of spectral measures. In particular, our results also apply to the isospectral Lax operator for the conservative Camassa-Holm flow and allow us to establish existence of global weak solutions with various step-like initial conditions of low regularity via the inverse spectral transform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01189 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Trace formulas and inverse spectral theory for generalized indefinite strings Eckhardt, Jonathan Kostenko, Aleksey Spectral Theory Primary 34A55, 34B07, Secondary 34L05, 37K15 Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and 2x2 canonical systems). We prove a number of Szegő-type theorems for generalized indefinite strings and related spectral problems (including Krein strings, canonical systems and Dirac operators). More specifically, for several classes of coefficients (that can be regarded as Hilbert-Schmidt perturbations of model problems), we provide a complete characterization of the corresponding set of spectral measures. In particular, our results also apply to the isospectral Lax operator for the conservative Camassa-Holm flow and allow us to establish existence of global weak solutions with various step-like initial conditions of low regularity via the inverse spectral transform. |
| title | Trace formulas and inverse spectral theory for generalized indefinite strings |
| topic | Spectral Theory Primary 34A55, 34B07, Secondary 34L05, 37K15 |
| url | https://arxiv.org/abs/2311.01189 |