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T1 - Characterizations of Herglotz-Nevanlinna Functions Using Positive Semi-Definite Functions and the Nevanlinna Kernel in Several Variables
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UR - http://hdl.handle.net/10138/334832
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A1 - Nedic, Mitja
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Y1 - 2021
LA - eng
AB - 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 w...
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KW - Herglotz-Nevanlinna functions; Positive semi-definite functions; Poisson-type functions; Nevanlinna kernel; MATRIX FUNCTIONS; OPERATOR; 111 Mathematics
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