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

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dc.contributor.author Nedic, Mitja
dc.date.accessioned 2021-10-01T12:34:01Z
dc.date.available 2021-10-01T12:34:01Z
dc.date.issued 2021-10
dc.identifier.citation 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
dc.identifier.other PURE: 168917735
dc.identifier.other PURE UUID: 2ac44cdb-f467-4c10-8b1b-bd9a722ec37b
dc.identifier.other WOS: 000695839500001
dc.identifier.other ORCID: /0000-0001-7867-5874/work/100872091
dc.identifier.uri http://hdl.handle.net/10138/334832
dc.description.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. en
dc.format.extent 29
dc.language.iso eng
dc.relation.ispartof Complex Analysis and Operator Theory
dc.rights cc_by
dc.rights.uri info:eu-repo/semantics/openAccess
dc.subject Herglotz-Nevanlinna functions
dc.subject Positive semi-definite functions
dc.subject Poisson-type functions
dc.subject Nevanlinna kernel
dc.subject MATRIX FUNCTIONS
dc.subject OPERATOR
dc.subject 111 Mathematics
dc.title Characterizations of Herglotz-Nevanlinna Functions Using Positive Semi-Definite Functions and the Nevanlinna Kernel in Several Variables en
dc.type Article
dc.contributor.organization Department of Mathematics and Statistics
dc.description.reviewstatus Peer reviewed
dc.relation.doi https://doi.org/10.1007/s11785-021-01155-x
dc.relation.issn 1661-8254
dc.rights.accesslevel openAccess
dc.type.version publishedVersion

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