Regularity of Finite Type Critical Points for Self-Adjoint Operators in Krein Space

Abstract

Following the work of Krein and Langer [11], the spectral function has become a basic tool in the study of self-adjoint operators in Krein spaces, cf. [2, §4.1], [5, §VIII 6], [12] and the references therein. The resulting spectral decompositions behave as in Hilbert space except near the (at most finite) set of critical points, where the spectral function is, at least initially, undefined. Our purpose is to study these critical points in situations that permit finite dimensional analysis. In particular, we shall give a number of finite dimensional tests for regularity of critical points.