Perturbation theory of multiparameter eigenvalue problems
Copyright policy )Perturbation theory of multiparameter eigenvalue problems
Let \(T_ r\) and \(V_{rs}\) be linear selfadjoint operators in Hilbert spaces \({\mathfrak H}_ r\). Let \(\lambda_ s\) be complex parameters. Then it is considered the multiparameter system \[ (T_ r+\sum^{k}_{s=1}\lambda_ sV_{rs})u_ r=0,\quad r=1,...,k. \] The main objective is to study the influence of perturbations for the operators \(T_ r\). It is assumed that the perturbed operators \(T_ r(\theta)\) depend holomorphically on a parameter \(\theta\). The behaviour of the eigenvalues and eigenvectors as functions of \(\theta\) is investigated.
- University of Dundee United Kingdom
Perturbation theory of linear operators, Applied Mathematics, multiparameter system, eigenvalues, eigenvectors, Spectrum, resolvent, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces, Analysis, influence of perturbations
Perturbation theory of linear operators, Applied Mathematics, multiparameter system, eigenvalues, eigenvectors, Spectrum, resolvent, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces, Analysis, influence of perturbations
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