Abstract
Selfadjoint relations in Pontryagin spaces do not possess a spectral family completely characterizing them in the way that selfadjoint relations in Hilbert spaces do. Here it is shown that a combination of a factorization of generalized Nevanlinna functions with the standard spectral family of selfadjoint relations in Hilbert spaces can function as a spectral family for selfadjoint relations in Pontryagin spaces. By this technique additive decompositions are established for generalized Nevanlinna functions and selfadjoint relations in Pontryagin spaces.
Dedicated to V.E. Katsnelson on the occasion of his 75th birthday
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Hassi, S., Wietsma, H.L. (2020). Spectral Decompositions of Selfadjoint Relations in Pontryagin Spaces and Factorizations of Generalized Nevanlinna Functions. In: Alpay, D., Fritzsche, B., Kirstein, B. (eds) Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory. Operator Theory: Advances and Applications(), vol 280. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-44819-6_16
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