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Keywords:
Herglotz-Nevanlinna function; Cauchy-type function; symmetric extension; Stieltjes inversion formula
Herglotz-Nevanlinna function; Cauchy-type function; symmetric extension; Stieltjes inversion formula
Summary:
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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