Characterizations of Herglotz-Nevanlinna Functions Using Positive Semi-Definite Functions and the Nevanlinna Kernel in Several Variables

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Nedic , M 2021 , ' Characterizations of Herglotz-Nevanlinna Functions Using Positive Semi-Definite Functions and the Nevanlinna Kernel in Several Variables ' , Complex Analysis and Operator Theory , vol. 15 , no. 7 , 109 . https://doi.org/10.1007/s11785-021-01155-x

Title: Characterizations of Herglotz-Nevanlinna Functions Using Positive Semi-Definite Functions and the Nevanlinna Kernel in Several Variables
Author: Nedic, Mitja
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2021-10
Language: eng
Number of pages: 29
Belongs to series: Complex Analysis and Operator Theory
ISSN: 1661-8254
URI: http://hdl.handle.net/10138/334832
Abstract: In this paper, we give several characterizations of Herglotz-Nevanlinna functions in terms of a specific type of positive semi-definite functions called Poisson-type functions. This allows us to propose a multidimensional analogue of the classical Nevanlinna kernel and a definition of generalized Nevanlinna functions in several variables. Furthermore, a characterization of the symmetric extension of a Herglotz-Nevanlinna function is also given. The subclass of Loewner functions is discussed as well, along with an interpretation of the main result in terms of holomorphic functions on the unit polydisk with non-negative real part.
Subject: Herglotz-Nevanlinna functions
Positive semi-definite functions
Poisson-type functions
Nevanlinna kernel
MATRIX FUNCTIONS
OPERATOR
111 Mathematics
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