Stability theorems for singular perturbation of eigenvalues

Abstract

Two stability, i.e., convergence in multiplicity, theorems for eigenvalues of non-self-adjoint singular perturbation problems are proved in this paper. Use is made of quadratic interpolation between Hubert spaces to obtain an extension of the notion of a holomorphic family of type (B). Applications to singular perturbation problems for non-self-adjoint elliptic partial differential operators, and to singular potential perturbation problems with complex coupling constants, are presented.