Functional Calculus for Definitizable Self-adjoint Linear Relations on Krein Spaces

In the present note a functional calculus for self-adjoint definitizable linear relations on Krein spaces is developed. This functional calculus is the proper analogue of in the Hilbert space situation where is a bounded and measurable function on and is defined in the weak sense. The derived functional calculus also comprises the Spectral Theorem for self-adjoint definitizable operators on Krein spaces showing the existence of spectral projections.