this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

The interior transmission problem is a boundary value problem that plays a basic role in inverse scattering theory but unfortunately does not seem to be included in any existing theory in partial differential equations.This paper presents old and new results for the interior transmission problem ,in particular its relation to inverse scattering theory and new results on the spectral theory asso...

We construct a class of matrix-valued Schrödinger operators with prescribed finite-band spectra of maximum spectral multiplicity. The corresponding matrix potentials are shown to be stationary solutions of the KdV hierarchy. The methods employed in this paper rely on matrix-valued Herglotz functions, Weyl–Titchmarsh theory, pencils of matrices, and basic inverse spectral theory for matrix-value...

We present a spectral and inverse spectral theory for the zero dispersion spectral problem associated with the Camassa-Holm equation. This is an alternative approach to that in [10] by Eckhardt and Teschl. Mathematics Subject Classification (2010). Primary 37K15, 34B40 ; Secondary 35Q35, 34L05.

We study inverse spectral analysis for finite and semi-infinite Jacobi matrices H. Our results include a new proof of the central result of the inverse theory (that the spectral measure determines H). We prove an extension of Hochstadt’s theorem (who proved the result in the case n = N) that n eigenvalues of an N ×N Jacobi matrix, H, can replace the first n matrix elements in determining H uniq...

We establish connections between four approaches to inverse spectral problems: the classical Gelfand–Levitan theory, the Simon theory, the approach proposed by Remling, and the Boundary Control method. We show that the Boundary Control approach provides simple and physically motivated proofs of the central results of other theories. We demonstrate also the connections between the dynamical and ...

We discuss direct and inverse spectral theory for the isospectral problem of the dispersionless Camassa–Holm equation, where the weight is allowed to be a finite signed measure. In particular, we prove that this weight is uniquely determined by the spectral data and solve the inverse spectral problem for the class of measures which are sign definite. The results are applied to deduce several fa...