Communications in Mathematical Sciences

Volume 22 (2024)

Number 6

Localization and the landscape function for regular Sturm-Liouville operators

Pages: 1733 – 1748

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n6.a12

Authors

Mirza Karamehmedović (Department of Applied Mathematics and Computer Science, Danmarks Tekniske Universitet, Lyngby, Denmark)

Faouzi Triki (Laboratoire Jean Kuntzmann-Bâtiment IMAG, Université Grenoble Alpes, Saint-Martin-d’Héres, France)

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.

Keywords

Sturm-Liouville theory, spectral theory

2010 Mathematics Subject Classification

34B09, 34B24

Full Text (PDF format)

Received 28 June 2023

Received revised 12 October 2023

Accepted 3 February 2024

Published 18 July 2024