A Variational Principle in Krein Space
Copyright policy )A Variational Principle in Krein Space
A variational characterization, involving a max-inf of the Rayleigh quotient, is established for certain eigenvalues of a wide class of definitizable selfadjoint operators Q in a Krein space. The operator Q may have continuous spectrum and nonreal and nonsemisimple eigenvalues; in particular it may have embedded eigenvalues. Various applications are given to selfadjoint linear and quadratic eigenvalue problems with weak definiteness assumptions.
indefinite inner-product, Variational methods for second-order elliptic equations, applications, Krein space, Hermitian and normal operators (spectral measures, functional calculus, etc.), Ritz-Rayleigh variational principle, Variational inequalities, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces, Variational methods for eigenvalues of operators
indefinite inner-product, Variational methods for second-order elliptic equations, applications, Krein space, Hermitian and normal operators (spectral measures, functional calculus, etc.), Ritz-Rayleigh variational principle, Variational inequalities, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces, Variational methods for eigenvalues of operators
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