Perturbation theory of multiparameter eigenvalue problems

AbstractWe investigate the multiparameter eigenvalue problem in the case where some of the operators depend holomorphically on a perturbation parameter. The behaviour of eigenvalues of finite multiplicity, together with the associated eigenvectors, is considered as the perturbation parameter is varied. In addition we discuss the effect of the perturbation on a complete orthonormal system of eigenvectors. The theory allows fairly general holomorphic perturbations and only requires a weak multiparameter “definiteness” condition