Results 211 to 220 of about 47,710 (235)
A new series expansion for slice regular functions
Advances in Mathematics, 2012 A promising theory of quaternion-valued functions of one quaternionic variable, now called slice regular functions, has been introduced in 2006. The basic examples of slice regular functions are power series centered at 0 on their balls of convergence. Conversely, if f is a slice regular function then it admits at each point of its domain an expansion ...
Caterina Stoppato
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Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions [PDF]
Journal of Geometric Analysis, 2021 In the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex ...
Guangbin Ren +2 more
exaly +4 more sources
s-Regular functions which preserve a complex slice [PDF]
Annali Di Matematica Pura Ed Applicata, 2018 We study global properties of quaternionic slice regular functions (also called extit{s-regular}) defined on symmetric slice domains. In particular, thanks to new techniques and points of view, we can characterize the property of being one-slice ...
Amedeo Altavilla, Chiara de Fabritiis
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On some splitting properties of slice regular functions
Complex Variables and Elliptic Equations, 2017 In this paper, we prove some splitting results for holomorphic functions of a complex variable and for slice regular functions of a quaternionic variable, in both cases on open domains having some specific properties of symmetry.
J OSCAR González-Cervantes +1 more
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A Cauchy kernel for slice regular functions [PDF]
Annals of Global Analysis and Geometry, 2009 In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present ...
Fabrizio Colombo +2 more
exaly +6 more sources
Slice regular functions of several octonionic variables [PDF]
Mathematical Methods in the Applied Sciences, 2020 A slice theory of several octonionic variables is introduced in the article as a generalization of the holomorphic theory of several complex variables. Our new trick is to focus our attentions on some subset of with the same complex structures. In our setting, the Bochner‐Martinelli formula and the Hartogs extension theorems are established for slice
Guangbin Ren, Ting Yang
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Some of the next articles are maybe not open access.
Slice Regular Functions: Algebra
2016This chapter contains the definition and some basic results on slice regular functions. In particular, we discuss the subclass of slice regular intrinsic functions which possess additional properties. This subclass contains the transcendental functions like the quaternionic exponential, sine and cosine. We also introduce a suitable multiplication and a
Fabrizio Colombo +2 more
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Slice Regular Functions: Analysis
2016In this chapter we study the analytic properties of slice regular functions. We start by illustrating the Cauchy and Schwarz integral formulas as well as some consequences. Then we prove a version of the Riemann mapping theorem, we discuss the properties of the zeros of slice regular functions and the Ehrenpreis-Malgrange lemma.
Fabrizio Colombo +2 more
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A Fiber Bundle over the Quaternionic Slice Regular Functions
Advances in Applied Clifford Algebras, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Growth of Entire Slice Regular Functions
2016In this chapter we study the growth of entire slice regular functions and we relate it with the coefficients of the power series expansion of a function. We prove some brand new results, like the Jensen and Caratheodory theorem. These results are not immediate extensions of the analogous results in the complex setting.
Fabrizio Colombo +2 more
openaire +1 more source