Nonlinear asymptotic mean value characterizations of holomorphic functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910471070679040 |
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| author | Durastanti, Riccardo Magnanini, Rolando |
| author_facet | Durastanti, Riccardo Magnanini, Rolando |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_08437 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonlinear asymptotic mean value characterizations of holomorphic functions Durastanti, Riccardo Magnanini, Rolando Analysis of PDEs Complex Variables 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. |
| title | Nonlinear asymptotic mean value characterizations of holomorphic functions |
| topic | Analysis of PDEs Complex Variables |
| url | https://arxiv.org/abs/2306.08437 |