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

Mitja Nedic — 2023

Czechoslovak Mathematical Journal

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.

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