We show that the classical Hamburger moment problem can be included in the spectral theory of generalized indefinite strings. Namely, we introduce the class of Kreinâ€“Langer strings and show thatâ€¦ (More)

We systematically develop Weylâ€“Titchmarsh theory for singular differential operators on arbitrary intervals (a, b) âŠ† R associated with rather general differential expressions of the type Ï„f = 1 r ( âˆ’â€¦ (More)

We provide an abstract framework for singular one-dimensional SchrÃ¶dinger operators with purely discrete spectra to show when the spectrum plus norming constants determine such an operatorâ€¦ (More)

We discuss direct and inverse spectral theory for the isospectral problem of the dispersionless Camassaâ€“Holm equation, where the weight is allowed to be a finite signed measure. In particular, weâ€¦ (More)

Building on work on Miuraâ€™s transformation by Kappeler, Perry, Shubin, and Topalov, we develop a detailed spectral theoretic treatment of SchrÃ¶dinger operators with matrix-valued potentials, withâ€¦ (More)

We develop singular Weylâ€“Titchmarshâ€“Kodaira theory for onedimensional Dirac operators. In particular, we establish existence of a spectral transformation as well as local Borgâ€“Marchenko andâ€¦ (More)

We give a comprehensive treatment of Sturmâ€“Liouville operators whose coefficients are measures including a full discussion of self-adjoint extensions and boundary conditions, resolvents, andâ€¦ (More)

We introduce a novel approach for defining a Î´â€²-interaction on a subset of the real line of Lebesgue measure zero which is based on Sturmâ€“ Liouville differential expression with measure coefficients.â€¦ (More)

We discuss direct and inverse spectral theory of self-adjoint Sturmâ€“ Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop singularâ€¦ (More)

We introduce a generalized isospectral problem for global conservative multi-peakon solutions of the Camassaâ€“Holm equation. Utilizing the solution of the indefinite moment problem given by M. G.â€¦ (More)