Global Perturbation of Nonlinear Eigenvalues

This paper generalizes the classical theory of perturbation of eigenvalues up to cover the most general setting where the operator surface L : [a, b] x [c, d] -> Phi(0)(U, V), (lambda, mu) bar right arrow L(lambda, mu), depends contin- uously on the perturbation parameter, mu, and holomorphically, as well as nonlinearly, on the spectral parameter, lambda, where Phi(0)(U, V) stands for the set of Fredholm operators of index zero between U and V. The main result is a substantial extension of a classical finite-dimensional theorem of T. Kato (see [T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Class. Math., Springer, Berlin, 1995, Chapter 2, Section 5]).

Automated summary

This paper generalizes the classical theory of perturbation of eigenvalues to cover the most general setting, resulting in a substantial extension of a classical finite-dimensional theorem.