On the eigenfunction expansion for Hamilton operators
Copyright policy )On the eigenfunction expansion for Hamilton operators
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 J -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.
- University of Vienna Austria
kink, asymptotic stability, Ginzburg-Landau equations, Ginzburg-Landau equation, NLS equations (nonlinear Schrödinger equations), Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, self-adjoint operator, eigenfunction expansion, generalized eigenfunction, Fermi Golden Rule, \(J\)-self-adjoint operator, Jordan block, secular solutions, eigenvector, Hamilton equation, spectral resolution, Krein space, spectral representation
kink, asymptotic stability, Ginzburg-Landau equations, Ginzburg-Landau equation, NLS equations (nonlinear Schrödinger equations), Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, self-adjoint operator, eigenfunction expansion, generalized eigenfunction, Fermi Golden Rule, \(J\)-self-adjoint operator, Jordan block, secular solutions, eigenvector, Hamilton equation, spectral resolution, Krein space, spectral representation
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