Spectral problems in inhomogeneous media, spectral parameter power series and transmutation operators

Abstract

We give a brief overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS) and propose a new method for numerical solution of corresponding spectral problems.

8 pages. arXiv admin note: substantial text overlap with arXiv:1203.4225

References in corpus (5)

• Transmutations, L-bases and complete families of solutions of the stationary Schrödinger equation in the plane
• Transmutations and spectral parameter power series in eigenvalue problems
• Transmutations for Darboux transformed operators with applications
• Spectral parameter power series representation for Hill's discriminant
• Eigenvalue problems, spectral parameter power series, and modern applications

Cited by in corpus (4)

• Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions
• Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems
• Spectral parameter power series for perturbed Bessel equations
• Construction of transmutation operators and hyperbolic pseudoanalytic functions