Journal of Operator Theory

Volume 55, Issue 1, Winter 2006 pp. 17-48.

Generalized Nevanlinna functions with essentially positive spectrum

Authors: Michael Kaltenbaeck (1), Henrik Winkler (2), and Harald Woracek (3)
Author institution: (1) Institut fuer Analysis und Scientific Computing, Technische Universitaet Wien, Vienna, 1040, Austria
(2) Faculteit der Wiskunde en Natuurwetenschappen, Rijksuniversiteit Groningen, Groningen, 9700 AV, The Netherlands
(3) Institut fuer Analysis und Scientific Computing, Technische Universitaet Wien, Vienna, 1040, Austria

Summary: We introduce an indefinite analogue of the so-called Stieltjes class and provide some basic results on this \textit{indefinite Stieltjes class}. Among them: The relation between the functions $q(z)$, $zq(z)$ and $zq(z^2)$, limit properties, a distributional representation. These results generalize well known properties of functions belonging to the Stieltjes class.

Keywords: Stieltjes class, indefinite inner product, distribution

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