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Realizations of meromorphic functions of bounded type

  • Emmel, Christian
Publication Date
Jan 01, 2023
DiVA - Academic Archive On-line
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A realization of a locally analytic function is basically a way of expressing the function in terms of the resolvent of a self-adjoint operator. In the classical Hilbert space setting realizations correspond in an essentially one-to-one way to Herglotz-Nevanlinna functions. Considering more generalobjects than Hilbert spaces, so called Krein spaces, opens up the possibility to address more general function classes. This thesis is concerned withrealizations and related minimality questions for meromorphic functionsof bounded type. In the general introduction we review preliminaries from complex anal-ysis and operator theory and give an idea how the main results of thesubsequent two articles relate to the already existing theory. In the first included article realizations for meromorphic functions ofbounded type are constructed. However, these realizations are not mini-mal in general. The second article is a first step in addressing this mini-mality question. There we focus on the well behaved subclass of atomic density functions for which minimal realizations are constructed.

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