On M. G. Krein's work in the theory of linear periodic Hamiltonian systems
type: Item
instance of: scholarly article
title: On M. G. Krein's work in the theory of linear periodic Hamiltonian systems
zbMATH Open document ID: 0852.70010
DOI: 10.1007/BF01057005
author: V. A. Yakubovich
published in: Ukrainian Mathematical Journal
publication date: 1995-11-02T00:00:00Z
review text: The study discusses the main ideas of the theory of linear periodic Hamiltonian systems, as based on numerous papers devoted to the investigation of the subject. The presentation is supported by a series of examples, from engineering and physical areas, with the observation that, before Krein, the problem was hardly investigated and few results were obtained on the Hill equation related to the motion of Moon. Also is discussed -- in a special paragraph -- the stability criterion for the linear periodic Hamiltonian equation with possible applications not only to central stability region but also to arbitrary stability regions. Another problem in which Krein was especially interested and to which he made a thorough analysis, was the boundary value problem, along with the phenomena of high-frequency stabilization, parametric resonance, etc. Close connections were established between the theory of linear Hamiltonian equations, the theory of operators in space with indefinite metrics, the inverse Sturm-Liouville problem and the theory of wave-guides.
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 01A70
zbMATH DE Number: 803822
zbMATH Keywords: Hill equation
zbMATH Keywords: stability criterion
zbMATH Keywords: stability regions
zbMATH Keywords: boundary value problem
zbMATH Keywords: high-frequency stabilization
zbMATH Keywords: parametric resonance
zbMATH Keywords: theory of operators in space with indefinite metrics
zbMATH Keywords: inverse Sturm-Liouville problem
zbMATH Keywords: theory of wave-guides
reviewed by: Cristina Irimia
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01057005
OpenAlex ID: W2026338181
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description: scientific article; zbMATH DE number 803822