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In the present note a functional calculus $\phi \mapsto \phi(A)$ forself-adjoint definitizable linear relation on Krein spaces is developed. Thisfunctional calculus is the proper analogue of $\phi \mapsto \int \phi \, dE$ inthe Hilbert space situation. It also comprises the Spectral Theorem forself-adjoint definitizable operators on Krein spaces showing the existence ofspectral projections.

Functional Calculus for definitizable self-adjoint linear relations on Krein spaces