On M. G. Krein's work in the theory of linear periodic Hamiltonian systems
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.
theory of operators in space with indefinite metrics
scientific article; zbMATH DE number 803822
scientific article