Localization and the landscape function for regular Sturm-Liouville operators

Mirza Karamehmedovic, Faouzi Triki

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Abstract

We consider the localization in the eigenfunctions of regular Sturm-Liouville operators. After deriving non-asymptotic and asymptotic lower and upper bounds on the localization coefficient of the eigenfunctions, we characterize the landscape function in terms of the first eigenfunction. Several numerical experiments are provided to illustrate the obtained theoretical results.
Original languageEnglish
JournalCommunications in Mathematical Sciences
Volume22
Issue number6
Pages (from-to)1733-1748
ISSN1539-6746
DOIs
Publication statusPublished - 2024

Keywords

  • Spectral theory
  • Sturm-Liouville theory

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