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On eigenfunction expansion of solutions to the Hamilton equations. (English) Zbl 1300.34195

The authors establish a spectral representation for solutions to linear Hamilton equations with positive definite energy in a Hilbert space. Their approach is a special version of M. Krein’s spectral theory of \(J\)-selfadjoint operators in Hilbert spaces with indefinite metric. Their main result is an application to the eigenfunction expansion for the linearized relativistic Ginzburg-Landau equation. It should be noted that the problem of eigenfunction expansion for the linearized relativistic Ginzburg-Landau equation has been studied early by the authors [Arch. Ration. Mech. Anal. 202, No. 1, 213–245 (2011; Zbl 1256.35146); Commun. Math. Phys. 302, No. 1, 225–252 (2011; Zbl 1209.35134)].

MSC:

34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
83A05 Special relativity
34A30 Linear ordinary differential equations and systems
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