Sturm-Liouville problems on graphs with Robin boundary conditions
Yuri Latushkin, Vyacheslav Pivovarchik, Alesia Supranovych
TL;DR
This paper investigates the spectral properties of Sturm-Liouville problems on graphs with Robin boundary conditions, providing asymptotic eigenvalue descriptions and methods to recover Robin coefficients from eigenvalues.
Contribution
It introduces new asymptotic formulas for eigenvalues and a technique to determine Robin boundary coefficients from spectral data on quantum graphs.
Findings
Derived asymptotic eigenvalue formulas for Robin boundary conditions.
Established a method to recover Robin coefficients from known eigenvalues.
Analyzed spectral characteristics of Sturm-Liouville problems on graphs.
Abstract
We study characteristic functions and describe asymptotics of the eigenvalues for the spectral Sturm-Liouville problem on graphs equipped with Robin-Kirhhoff boundary conditions. Also, we show how to recover the coefficients in the Robin conditions for the quantum graphs provided the shape of the graphs and some Robin eigenvalues are known.
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