Abstract
We present explicit realizations in terms of self-adjoint operators and linear relations for a non-zero scalar generalized Nevanlinna function N(z) and the function \( \hat N \) (z) = −1/N(z) under the assumption that \( \hat N \) (z) has exactly one generalized pole which is not of positive type namely at z = ∞. The key tool we use to obtain these models is reproducing kernel Pontryagin spaces.
To Heinz Langer, wishing him a happy retirement
The authors gratefully acknowledge support from the “Fond zur Förderung der wissenschaftlichen Forschung” (FWF, Austria, grant number P15540-N05), the Netherlands Organization for Scientific Research NWO (grant NWO 047-008-008), and the Research Training Network HPRNCT-2000-00116 of the European Union.
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Dijksma, A., Luger, A., Shondin, Y. (2005). Minimal Models for \( \mathcal{N}_\kappa ^\infty \) -functions. In: Langer, M., Luger, A., Woracek, H. (eds) Operator Theory and Indefinite Inner Product Spaces. Operator Theory: Advances and Applications, vol 163. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7516-7_5
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