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Characterization theorems for bounded and positive two‐variable functions
Author(s) -
Delsarte Ph.,
Genin Y.,
Kamp Y.
Publication year - 1979
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490070212
Subject(s) - bounded function , mathematics , variable (mathematics) , rational function , sequence (biology) , analytic function , extension (predicate logic) , class (philosophy) , representation (politics) , characterization (materials science) , pure mathematics , bounded deformation , degree (music) , discrete mathematics , uniform boundedness , mathematical analysis , computer science , genetics , materials science , physics , acoustics , law , biology , programming language , nanotechnology , artificial intelligence , politics , political science
Abstract The aim of this paper is a two‐variable extension of some classical results by Carathéodory and Schur, characterizing the classes of positive and bounded analytic functions. It is shown how these functions can be approximated by a convergent sequence of polynomials of the same class. The particular case where bounded two‐variable functions reduce to rational inner functions is described. As an application, the integral representation of positive functions is used to generate the complete family of two‐variable reactances of the first degree.