Inverse Spectral and Scattering Theory for the Half-Line Left-Definite Sturm–Liouville Problem

DOI10.1137/080724575zbMath1178.37095OpenAlexW2078554282MaRDI QIDQ3398282

Christer Bennewitz, Rudi Weikard, B. Malcolm Brown

Publication date: 28 September 2009

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/080724575

zbMATH Keywords

inverse spectral problemsSturm-Liouville equationinverse scattering problems

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Inverse problems involving ordinary differential equations (34A55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (15)

A uniqueness result for one-dimensional inverse scattering ⋮ The inverse spectral problem for indefinite strings ⋮ Minimization of lowest positive periodic eigenvalue for the Camassa–Holm equation with indefinite potential ⋮ The Critical Point Infinity Associated with Indefinite Sturm–Liouville Problems ⋮ Direct and inverse spectral theory of singular left-definite Sturm-Liouville operators ⋮ Scattering and inverse scattering for a left-definite Sturm-Liouville problem ⋮ The inverse resonance problem for left-definite Sturm-Liouville operators ⋮ Singular left-definite Hamiltonian systems in the Sobolev space ⋮ The inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data ⋮ An isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation ⋮ Unique solvability of a coupling problem for entire functions ⋮ Dependence of eigenvalues on the boundary conditions of Sturm-Liouville problems with one singular endpoint ⋮ On the absolutely continuous spectrum of generalized indefinite strings ⋮ On the absolutely continuous spectrum of generalized indefinite strings. II ⋮ Quadratic operator pencils associated with the conservative Camassa-Holm flow

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