On Eigenfunction Expansion of Solutions to the Hamilton Equations

We establish a spectral representation for solutions to linear Hamilton equations with positive definite energy in a Hilbert space. Our approach is a special version of M. Krein’s spectral theory of J -selfadjoint operators in the Hilbert spaces with indefinite metric. Our main result is an applicat...

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Bibliographic Details
Published in:Journal of statistical physics Vol. 154; no. 1-2; pp. 503 - 521
Main Authors: Komech, A., Kopylova, E.
Format: Journal Article
Language:English
Published: Boston Springer US 01.01.2014
Springer
Subjects:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Eigenfunction expansion
Asymptotic stability
Generalized eigenfunction
Selfadjoint operator
Ginzburg–Landau equation
Spectral resolution
Eigenvector
Hamilton equation
Krein space
Kink
Fermi golden rule
Spectral representation
ISSN:0022-4715, 1572-9613
Online Access:Get full text
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Summary:We establish a spectral representation for solutions to linear Hamilton equations with positive definite energy in a Hilbert space. Our approach is a special version of M. Krein’s spectral theory of J -selfadjoint operators in the Hilbert spaces with indefinite metric. Our main result is an application to the eigenfunction expansion for the linearized relativistic Ginzburg–Landau equation.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-013-0846-1