Semiclassical asymptotics of the vector Sturm-Liouville problem
type: Item
instance of: scholarly article
title: Semiclassical asymptotics of the vector Sturm-Liouville problem
zbMATH Open document ID: 1124.34061
DOI: 10.1134/S1061920806020051
published in: Russian Journal of Mathematical Physics
publication date: 2007-03-26T00:00:00Z
review text: The paper deals with the matrix Sturm-Liouville problem on the whole line with a potential which is a smooth, self-adjoint matrix function, and with a small parameter at the derivatives. The goal is to study the asymptotics of eigenvalues and eigenfunctions in the case when the symbol of the problem has eigenvalues of variable multiplicity. The main result is that in the nonresonant case, the Born-Sommerfeld-Maslov quantization conditions provide the asymptotics of eigenvalues with quadratic precision, as in the case in which there is no modification of multiplicity. In the case of nontrivial multiplicity, the asymptotic behavior of the eigenfunctions is different.
Mathematics Subject Classification ID: 34L20
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 81Q20
zbMATH DE Number: 5136621
zbMATH Keywords: matrix Sturm-Liouville problem
zbMATH Keywords: WKB asymptotics, multiphase asymptotics
zbMATH Keywords: quantization conditions
author: Andriy Kryvko
author: Valeri V. Kucherenko
reviewed by: Dmitry Shepelsky
MaRDI profile type: Publication
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full work available at URL: s1061920806020051
OpenAlex ID: W2038043515
description: scientific article; zbMATH DE number 5136621