Spectral Theorem for Definitizable Normal Linear Operators on Krein Spaces

In the present note a spectral theorem for normal definitizable linear operators on Krein spaces is derived by developing a functional calculus ({phi mapsto phi(N)}) which is the proper analogue of ({phi mapsto int phi , dE}) in the Hilbert space situation. This paper is the first systematical study of definitizable normal operators on Krein spaces.