The generalized Fourier transform associated with a selfadjoint Sturm–Liouville operator is a unitary transformation which converts the action of this operator into a simple product by a spectral variable. For a particular operator defined on the half-line and which involves a step function, we show how to extend such a transformation to generalized functions, or distributions, with a suitable ...

Inverse spectral problems consist in recovering operators from their spectral characteristics. Such problems play an important role in mathematics and have many applications in natural sciences (see, for example, [1 – 6]). In 1988, the inverse nodal problem was posed and solved for Sturm-Liouville problems by J. R. McLaughlin [7], who showed that the knowledge of a dense subset of nodal points ...

We classify the general linear boundary conditions involving u′′, u′ and u on the boundary {a, b} so that a Sturm-Liouville operator on [a, b] has a unique self-adjoint extension on a suitable Hilbert space.

We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we show that the corresponding self-adjoint differential operator in a Krein space locally has the same spectral properties as a definitizable operator.

We propose a numerical algorithm for solving inverse problems of spectral analysis for Sturm–Liouville differential operators on the half-line. Moreover some results of numerical experiments are also presented. AMS subject classification: 65L09, 34A55, 47E05.

— In this work, we use the regularized sampling method to compute the eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval. We work out an example by computing a few eigenvalues and their corresponding eigenfunctions.

This article presents an overview of the recent literature and summarises the major theoretical developments pertaining to a class of non-Sturm-Liouville orthogonality relations relevant to fluid-structure interaction.

We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator ?4 d 2 ds 2 + 2 (s) with potential given by the curvature of a closed curve.

In this study we investigate asymptotic behavior of eigenvalues and eigenfunctions of one discontinuous Sturm-Liouville problem with eigendependent boundary and transmission conditions. c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.

We discuss integral estimates for domain of solutions to some canonical Riccati and Sturm–Liouville equations on the line. The approach is applied to Hardy and Poincaré type inequalities with weights.