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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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A note on the Bieberbach conjecture for some classes of slice regular functions [PDF]
, 2021 In this note we prove the Bieberbach conjecture for some classes of quaternionic functions, including quaternionic slice regular functions with specific geometric properties such as starlike and convex functions.
Fabio Vlacci +3 more
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On Fiber Bundles and Quaternionic Slice Regular Functions
Complex Analysis and Operator Theory, 2022 The papers \cite{O1,O2} are the first works to apply the theory of fiber bundles in the study of the quaternionic slice regular functions. The main goal of the present work is to extend the results given in \cite{O1}, where the quaternionic right linear space of quaternionic slice regular functions was presented as the base space of a fiber bundle ...
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Singularities of slice regular functions [PDF]
Mathematische Nachrichten, 2012 AbstractBeginning in 2006, G. Gentili and D. C. Struppa developed a theory of regular quaternionic functions with properties that recall classical results in complex analysis. For instance, in each Euclidean ball B(0, R) centered at 0 the set of regular functions coincides with that of quaternionic power series converging in B(0, R).
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A Bloch-Landau Theorem for Slice Regular Functions [PDF]
, 2013 The Bloch-Landau Theorem is one of the basic results in the geometric theory of holomorphic functions. It establishes that the image of the open unit disc $\mathbb{D}$ under a holomorphic function $f$ (such that $f(0)=0$ and $f'(0)=1$) always contains an open disc with radius larger than a universal constant.
Della Rocchetta, Chiara +2 more
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Julia theory for slice regular functions [PDF]
Transactions of the American Mathematical Society, 2016 Slice regular functions have been extensively studied over the past decade, but much less is known about their boundary behavior. In this paper, we initiate the study of Julia theory for slice regular functions. More specifically, we establish the quaternionic versions of the Julia lemma, the Julia-Carathéodory theorem, the ...
Ren, Guangbin, Wang, Xieping
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On Some Quaternionic Generalized Slice Regular Functions
Advances in Applied Clifford Algebras, 2022 The quaternionic valued functions of a quaternionic variable, often referred to as slice regular functions has been studied extensively due to the large number of generali\-zed results of the theory of one complex variable, see \cite{cgs,CSS,GSC,GS2,gssbook,gp,gpr,GS} and the references given there.
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Slice regular functions (Gentili er al., 2022) : Quaternions
, 2023 This thesis constitutes a comprehensive study of the fundamental properties of an analytic function theory over quaternions, which is known as slice regularity, as introduced in Gentili et al. (Gentili et al., 2022). In 2006, an approach to analysis over
Fathian Pourkondori, Mitra
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Entire slice regular functions
, 2015 Entire functions in one complex variable are extremely relevant in several areas ranging from the study of convolution equations to special functions. An analog of entire functions in the quaternionic setting can be defined in the slice regular setting, a framework which includes polynomials and power series of the quaternionic variable.
Colombo, Fabrizio +2 more
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