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

2021/02/16 by Mitja Nedic, Nedic, Mitja
Mathematics · #32A26 #32A99 #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2102.08031

openalex publication_date 2021/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive an analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function in several variables. Here, the main tools used are the so-called variable non-dependence property and the symmetry formula satisfied by Herglotz-Nevanlinna function and Cauchy-type functions. We also provide an extension of the Stieltjes inversion formula for Cauchy-type functions.

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