The inverse spectral problem for canonical systems
type: Item
instance of: scholarly article
title: The inverse spectral problem for canonical systems
zbMATH Open document ID: 0843.34031
DOI: 10.1007/BF01378784
published in: Integral Equations and Operator Theory
publication date: 1996-03-05T00:00:00Z
review text: The two dimensional canonical system is connected with the Hamiltonian \(H\), a real symmetric nonnegative trace normed \(2 \times 2\) matrix function on \([0, \infty)\). At \(\infty\) the Weyl's limit point case prevails. The corresponding Weyl coefficient belongs to \(\widetilde N : = N \cup \{\infty\}\), where \(N\) is the set of Nevanlinna functions. It is shown that any \(Q \in \widetilde N\) is a Weyl coefficient of a unique canonical system and that this proposition follows from some results of L. de Branges concerning Hilbert spaces of entire functions. It is mentioned that the basic ideas for the proof are contained in an unpublished article of M. G. Krejn and H. Langer. The construction of \(H\) is described when the given spectral measure of \(\mathbb{Q}\) has a density \(p (\lambda)^{-1}\), where \(p\) is a polynomial, positive on \(\mathbb{R}\). This is analogous to a method proposed by M. G. Krejn of constructing the mass distribution function of a string, if the main spectral function has a density of the same form.
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 47A75
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 845916
zbMATH Keywords: two dimensional canonical system
zbMATH Keywords: Weyl's limit point case
zbMATH Keywords: Weyl coefficient
zbMATH Keywords: spectral measure
author: Henrik Winkler
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01378784
OpenAlex ID: W2090802603
description: scientific article; zbMATH DE number 845916