Monogenic functions and harmonic vectors

Autor:	Sergiy Plaksa
Jazyk:	English<br />Ukrainian
Rok vydání:	2023
Předmět:	monogenic function harmonic function harmonic vector gateaux derivative topological vector space commutative multiplication Mathematics QA1-939
Zdroj:	Pracì Mìžnarodnogo Geometričnogo Centru, Vol 16, Iss 1, Pp 59-77 (2023)
Druh dokumentu:	article
ISSN:	2072-9812 2409-8906
DOI:	10.15673/tmgc.v16i1.2385
Popis:	We consider special topological vector spaces with a commutative multiplication for some of elements of the spaces and monogenic functions taking values in these spaces. Monogenic functions are understood as continuous and differentiable in the sense of G\^ateaux functions. We describe relations between the mentioned monogenic functions and harmonic vectors in the three-dimensional real space and establish sufficient conditions for infinite monogeneity of functions. Unlike the classical complex analysis, it is done in the case where the validity of the Cauchy integral formula for monogenic functions remains an open problem.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/b4f5633886cf461883d491c7a8cdba12 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF