Cauchy Problems for Discrete Holomorphic Functions

We solve Cauchy problems for discrete holomorphic functions defined on the Gaussian integers, which leads to the existence of discrete holomorphic functions with arbitrarily fast growth. This proves that certain classes of functions are closed in the sense of mathematical morphology.

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Veröffentlicht in:	Complex analysis and operator theory 2021-02, Vol.15 (1), Article 3
1. Verfasser:	Kiselman, Christer Oscar
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Analytic functions Cauchy problems Discrete holomorphic functions Duality of convolution operators In memory of Carlos A. Berenstein (1944-2019) Matematik Mathematical analysis Mathematical morphology Mathematics Mathematics and Statistics Operator Theory
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Beschreibung
Zusammenfassung:	We solve Cauchy problems for discrete holomorphic functions defined on the Gaussian integers, which leads to the existence of discrete holomorphic functions with arbitrarily fast growth. This proves that certain classes of functions are closed in the sense of mathematical morphology.
ISSN:	1661-8254 1661-8262 1661-8262
DOI:	10.1007/s11785-020-01025-y