Results 21 to 30 of about 21,179 (236)
A Local Cauchy Integral Formula for Slice-Regular Functions
Computational Methods and Function Theory, 2023 AbstractWe prove a local Cauchy-type integral formula for slice-regular functions. The formula is obtained as a corollary of a general integral representation formula where the integration is performed on the boundary of an open subset of the quaternionic space, with no requirement of axial symmetry.
Perotti, Alessandro
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A Phragmén - Lindelöf principle for slice regular functions
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2011 The celebrated 100-year old Phragmen-Lindelof principle is a far reaching extension of the maximum modulus theorem for holomorphic functions of one complex variable. In some recent papers there has been a resurgence of interest in principles of this type for functions of a hypercomplex variable and for solutions of suitable partial differential ...
GENTILI, GRAZIANO +2 more
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Slice Regular Functions as Covering Maps and Global $$\star $$-Roots
The Journal of Geometric Analysis, 2022 AbstractThe aim of this paper is to prove that a large class of quaternionic slice regular functions result to be (ramified) covering maps. By means of the topological implications of this fact and by providing further topological structures, we are able to give suitable natural conditions for the existence of k-th $$\star $$ ⋆
Altavilla A., Mongodi S.
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On the real differential of a slice regular function [PDF]
Advances in Geometry, 2018 Abstract In this paper we show that the real differential of any injective slice regular function is everywhere invertible. The result is a generalization of a theorem proved by G. Gentili, S. Salamon and C. Stoppato and it is obtained thanks, in particular, to some new information regarding the first coefficients of a certain polynomial
Amedeo Altavilla, Altavilla A.
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On a Criterion of Local Invertibility and Conformality for Slice Regular Quaternionic Functions [PDF]
Proceedings of the Edinburgh Mathematical Society, 2018 AbstractA new criterion for local invertibility of slice regular quaternionic functions is obtained. This paper is motivated by the need to find a geometrical interpretation for analytic conditions on the real Jacobian associated with a slice regular function f.
Anna Gori, Fabio Vlacci
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Dunkl approach to slice regular functions
Annali di Matematica Pura ed Applicata (1923 -)Abstract In this paper, we establish a connection between Dunkl analysis and slice analysis in the setting of Clifford algebras. Specifically, we show that a Clifford algebra-valued function is slice if, and only if, it belongs to the kernel of the Dunkl-spherical Dirac operator and that a slice function is slice regular if, and only ...
Giulio Binosi, Hendrik De Bie, Pan Lian
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Carathéodory Theorems for Slice Regular Functions [PDF]
Complex Analysis and Operator Theory, 2014 In this paper a quaternionic sharp version of the Carathéodory theorem is established for slice regular functions with positive real part, which strengthes a weaken version recently established by D. Alpay et. al. using the Herglotz integral formula.
Ren, Guangbin, Wang, Xieping
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Adaptive Fourier Decomposition of Slice Regular Functions
Advances in Applied Clifford Algebras, 2022 In the slice Hardy space over the unit ball of quaternions, we introduce the slice hyperbolic backward shift operator $\mathcal S_a$ with the decomposition process $$f=e_a\langle f, e_a\rangle+B_{a}*\mathcal S_a f,$$ where $e_a$ denotes the slice normalized Szegö kernel and $ B_a $ the slice Blaschke factor. Iterating the above decomposition process, a
Ming Jin +3 more
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The Schwarz-Pick lemma for slice regular functions [PDF]
Indiana University Mathematics Journal, 2012 The celebrated Schwarz-Pick lemma for the complex unit disk is the basis for the study of hyperbolic geometry in one and in several complex variables. In the present paper, we turn our attention to the quaternionic unit ball B. We prove a version of the Schwarz-Pick lemma for self-maps of B that are slice regular, according to the definition of Gentili
Bisi, Cinzia, STOPPATO, CATERINA
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Extension theorem and representation formula in non-axially-symmetric domains for slice regular functions [PDF]
, 2023 Slice analysis is a generalization of the theory of holomorphic functions of one complex variable to quaternions. Among the new phenomena which appear in this context, there is the fact that the convergence domain of f(q) = Sigma(n is an element of N) (q
Sabadini I., Ren G., Dou X.
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