On the eigenfunction expansion for Hamilton operators

  • Alexander I. Komech

    Universität Wien, Austria
  • Elena A. Kopylova

    Universität Wien, Austria

Abstract

A spectral representation for solutions to linear Hamilton equations with nonnegative energy in Hilbert spaces is obtained. This paper continues our previous work on Hamilton equations with positive definite energy. Our approach is a special version of M. Krein's spectral theory of JJ-selfadjoint operators in Hilbert spaces with indefinite metric.

As a principal application of these results, we justify the eigenfunction expansion for linearized nonlinear relativistic Ginzburg–Landau equations.

Cite this article

Alexander I. Komech, Elena A. Kopylova, On the eigenfunction expansion for Hamilton operators. J. Spectr. Theory 5 (2015), no. 2, pp. 331–361

DOI 10.4171/JST/100