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Generalized partial-slice monogenic functions.

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Název:	Generalized partial-slice monogenic functions.
Autoři:	Xu, Zhenghua¹ (AUTHOR), Sabadini, Irene² (AUTHOR)
Zdroj:	Transactions of the American Mathematical Society. Feb2025, Vol. 378 Issue 2, p851-883. 33p.
Témata:	TRANSFORMATION groups, IDENTITIES (Mathematics), MONOGENIC functions, CONFORMAL invariants, *LAURENT series
Abstrakt:	The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been studied. The main purpose of this article is to describe a new function theory which includes both of them as special cases. This theory allows to prove nice properties such as the identity theorem, a Representation Formula, the Cauchy (and Cauchy-Pompeiu) integral formula, the maximum modulus principle, a version of the Taylor series and Laurent series expansions. As a complement, we shall also offer two approaches to these functions via generalized partial-slice functions and via global differential operators. In addition, we discuss the conformal invariance property under a proper group of Möbius transformations preserving the partial symmetry of the involved domains. [ABSTRACT FROM AUTHOR]
Databáze:	Academic Search Index

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Abstrakt:	The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been studied. The main purpose of this article is to describe a new function theory which includes both of them as special cases. This theory allows to prove nice properties such as the identity theorem, a Representation Formula, the Cauchy (and Cauchy-Pompeiu) integral formula, the maximum modulus principle, a version of the Taylor series and Laurent series expansions. As a complement, we shall also offer two approaches to these functions via generalized partial-slice functions and via global differential operators. In addition, we discuss the conformal invariance property under a proper group of Möbius transformations preserving the partial symmetry of the involved domains. [ABSTRACT FROM AUTHOR]
ISSN:	00029947
DOI:	10.1090/tran/9356