A Cauchy Transform for Polymonogenic Functions on Fractal Domains

被引：0
作者：
Gomez Santiesteban, Tania Rosa [1 ]
Abreu Blaya, Ricardo [1 ]
Hernandez Gomez, Juan C. [1 ]
Sigarreta Almira, Jose Maria [1 ]
机构：
[1] Univ Autonoma Guerrero, Unidad Acad Matemat, Ave Lazaro Cardenas, Chilpancingo 39087, Guerrero, Mexico
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2022年 / 16卷 / 03期
关键词：
Polymonogenic functions; Cauchy formula; Fractals; INTEGRAL-OPERATORS;
D O I：
10.1007/s11785-022-01228-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A Cauchy integral representation formula for polymonogenic functions has been established in smoothly bounded domains, but the method by which it has been obtained cannot be extended to the case of domains with fractal boundary. In this paper an alternative polymonogenic Cauchy transform is defined, which enables us to obtain several types of integral representation formulae, including the Cauchy and Borel-Pompeiu representations in this very general geometric setting.
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页数：16
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