Sturm-Liouville systems with rational Weyl functions: Explicit formulas and applications
type: Item
instance of: scholarly article
title: Sturm-Liouville systems with rational Weyl functions: Explicit formulas and applications
zbMATH Open document ID: 0897.34025
DOI: 10.1007/BF01195588
author: I. Gohberg
author: Marinus Kaashoek
author: Alexander L. Sakhnovich
published in: Integral Equations and Operator Theory
publication date: 1998-10-19T00:00:00Z
review text: The authors solve explicitly direct and inverse spectral problems for Sturm-Liouville systems with rational Weyl functions, of the form \[ {d^2\over dx^2} f(x,\lambda)- u(x)f(x, \lambda)+ \lambda f(x,\lambda)= 0\tag{1} \] on the half axis \(x\geq 0\); \(f\) is a \(\mathbb{C}^m\)-valued function, \(u\) is an \(m\times m\) locally summable matrix function on \([0,+\infty)\) and \(\lambda\) is a complex spectral parameter. With system (1), the authors associate the symmetric operator \(H_0\) defined by \[ (H_0 f)(x):= -{d^2\over dx^2} f(x)+ u(x)f(x),\quad x\geq 0 \] and consider the spectral theory to (1) in terms of an isometric diagonalizing operator \(U\) such that \((U H_0f)(z)= z(Uf)(z)\).
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 93A99
zbMATH DE Number: 1140090
zbMATH Keywords: direct and inverse spectral problems
zbMATH Keywords: Sturm-Liouville systems
zbMATH Keywords: rational Weyl functions
reviewed by: Abdelkader Boucherif
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1140090