Abstract
We consider a scalar Nevanlinna-Pick interpolation problem with finitely many data and assume that the Pick matrix P is invertible and has k negative eigenvalues. We look for solutions of this problem in the class of meromorphic functions whose Nevanlinna kernel has k negative squares. The set of these solutions can be written as a fractional linear transformation of a parameter in the class of Nevanlinna functions, much as in the case K = 0. But now not the whole Nevanlinna class can be used as a parameter set. Our results are obtained through the characterization of the selfadjoint extensions of a symmetric operator in a Pontryagin space with both defect numbers equal to 1 in terms of a so called it-resolvent matrix.
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Dijksma, A., Langer, H. (1997). Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions. In: Dym, H., Katsnelson, V., Fritzsche, B., Kirstein, B. (eds) Topics in Interpolation Theory. Operator Theory Advances and Applications, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8944-5_4
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