Czechoslovak Mathematical Journal, first online, pp. 1-18


An analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function

Mitja Nedic

Received December 8, 2021.   Published online August 4, 2022.   OPEN ACCESS

Abstract:  We derive an analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function. Here, the main tools used are the so-called variable non-dependence property and the symmetry formula satisfied by Herglotz-Nevanlinna and Cauchy-type functions. We also provide an extension of the Stieltjes inversion formula for Cauchy-type and quasi-Cauchy-type functions.
Keywords:  Herglotz-Nevanlinna function; Cauchy-type function; symmetric extension; Stieltjes inversion formula
Classification MSC:  32A36, 32A99
DOI:  10.21136/CMJ.2022.0455-21

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Affiliations:   Mitja Nedic, Department of Mathematics and Statistics, University of Helsinki, PO Box 68, FI-00014 Helsinki, Finland, orc-id: 0000-0001-7867-5874, e-mail: mitja.nedic@helsinki.fi


 
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