Spectral parameter power series representation for Hill's discriminant

Abstract

We establish a series representation of the Hill discriminant based on the spectral parameter power series (SPPS) recently introduced by V. Kravchenko. We also show the invariance of the Hill discriminant under a Darboux transformation and employing the Mathieu case the feasibility of this type of series for numerical calculations of the eigenspectrum

13 pages, 2 figures, 19 references with titles, a few minor changes in the text

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• Nonlocal supersymmetric deformations of periodic potentials
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Periodic Sturm-Liouville problems related to two Riccati equations of constant coefficients
• An amplitude-phase (Ermakov-Lewis) approach for the Jackiw-Pi model of bilayer graphene

Cited by in corpus (12)

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• Soliton defects in one-gap periodic system and exotic supersymmetry
• One-parameter families of supersymmetric isospectral potentials from Riccati solutions in function composition form
• Complete systems of recursive integrals and Taylor series for solutions of Sturm-Liouville equations
• Spectral parameter power series for polynomial pencils of Sturm-Liouville operators and Zakharov-Shabat systems
• Analytic approximation of transmutation operators and related systems of functions
• Spectral problems in inhomogeneous media, spectral parameter power series and transmutation operators
• Supersymmetric generalized power functions
• On Sturm-Liouville Equations with Several Spectral Parameters