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.
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This research was partially supported by NSF Grant 02 MCS-7902663
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Greenlee, W.M. Stability theorems for singular perturbation of eigenvalues. Manuscripta Math 34, 157–174 (1981). https://doi.org/10.1007/BF01165534
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DOI: https://doi.org/10.1007/BF01165534