Nonlinear asymptotic mean value characterizations of holomorphic functions

Starting from a characterization of holomorphic functions in terms of a suitable mean value property, we build some nonlinear asymptotic characterizations for complex-valued solutions of certain nonlinear systems, which have to do with the classical Cauchy-Riemann equations. From these asymptotic ch...

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Bibliographic Details
Published in:arXiv.org 2024-05
Main Authors: Durastanti, Riccardo, Magnanini, Rolando
Format: Article
Language:English
Subjects:
Analytic functions
Asymptotic properties
Cauchy-Riemann equations
Mathematical analysis
Nonlinear systems
Online Access:Get full text
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Summary:Starting from a characterization of holomorphic functions in terms of a suitable mean value property, we build some nonlinear asymptotic characterizations for complex-valued solutions of certain nonlinear systems, which have to do with the classical Cauchy-Riemann equations. From these asymptotic characterizations, we derive suitable asymptotic mean value properties, which are used to construct appropriate vectorial dynamical programming principles. The aim is to construct approximation schemes for the so-called contact solutions, recently introduced by N. Katzourakis, of the nonlinear systems here considered.
ISSN:2331-8422
DOI:10.48550/arxiv.2306.08437