Limiting eigenfunctions of Sturm–Liouville operators subject to a spectral flow

We examine the spectrum of a family of Sturm–Liouville operators with regularly spaced delta function potentials parametrized by increasing strength. The limiting behavior of the eigenvalues under this spectral flow was described by Berkolaiko et al. (Lett Math Phys 109(7):1611–1623, 2019), where it...

Full description

Saved in:
Bibliographic Details
Published inAnnales mathématiques du Québec Vol. 45; no. 2; pp. 249 - 269
Main Authors Beck, Thomas, Bors, Isabel, Conte, Grace, Cox, Graham, Marzuola, Jeremy L.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2021
Springer Nature B.V
Subjects
Algebra
Analysis
Constraining
Delta function
Eigenvalues
Eigenvectors
Mathematics
Mathematics and Statistics
Number Theory
Operators (mathematics)
Spectra
34B24
35P05
Nodal partitions
34C10
34L05
Spectral flows
Nodal deficiency
Sturm-Liouville operators
Online AccessGet full text
ISSN2195-4755
2195-4763
DOI10.1007/s40316-020-00142-6

Cover

More Information
Summary:We examine the spectrum of a family of Sturm–Liouville operators with regularly spaced delta function potentials parametrized by increasing strength. The limiting behavior of the eigenvalues under this spectral flow was described by Berkolaiko et al. (Lett Math Phys 109(7):1611–1623, 2019), where it was used to study the nodal deficiency of Laplacian eigenfunctions. Here we consider the eigenfunctions of these operators. In particular, we give explicit formulas for the limiting eigenfunctions, and also characterize the eigenfunctions and eigenvalues for all values for the spectral flow parameter (not just in the limit). We also develop spectrally accurate numerical tools for comparison and visualization.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2195-4755
2195-4763
DOI:10.1007/s40316-020-00142-6