Abstract
In the present note a functional calculus $${\phi \mapsto \phi(A)}$$ for self-adjoint definitizable linear relations on Krein spaces is developed. This functional calculus is the proper analogue of $${\phi \mapsto \int \phi \, dE}$$ in the Hilbert space situation where $${\phi}$$ is a bounded and measurable function on $${\sigma(A)}$$ and $${\int \phi \, dE}$$ 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.
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