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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Dedicated to Heinz Langer on the occasion of his 80th birthday.
This work was supported by a joint project of the Austrian Science Fund (FWF, I1536–N25) and the Russian Foundation for Basic Research (RFBR, 13-01-91002-ANF).
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Kaltenbäck, M., Pruckner, R. Functional Calculus for Definitizable Self-adjoint Linear Relations on Krein Spaces. Integr. Equ. Oper. Theory 83, 451–482 (2015). https://doi.org/10.1007/s00020-015-2262-1
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DOI: https://doi.org/10.1007/s00020-015-2262-1