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M. Kaltenbäck, R. Pruckner:
"Functional Calculus for definitizable self-adjoint linear relations on Krein spaces";
in: "ASC Report 06/2015", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2015, ISBN: 978-3-902627-08-7, 1 - 27.

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

Krein space, definitizable linear relations, spectral theorem.

http://www.asc.tuwien.ac.at/preprint/2015/asc06x2015.pdf