Spectral Dependence on a Parameter

Abstract

The following theorem on the representation of zeros of an analytic function in two variables is well known, however often formulated in slightly different forms. For the sake of completeness and to have it in exactly the form we need it, the theorem and its proof are given below. For slightly different formulations and proofs we refer the reader to [25, Appendix A 5.4, Theorem 3], [114, Section A.1, Lemma A.1.3] and [185, Section 45, Corollary, p. 303].