Results 11 to 20 of about 47,710 (235)
$*$-exponential of slice-regular functions [PDF]
Proceedings of the American Mathematical Society, 2018 According to [5] we define the $*$-exponential of a slice-regular function, which can be seen as a generalization of the complex exponential to quaternions. Explicit formulas for $\exp_*(f)$ are provided, also in terms of suitable sine and cosine functions.
Altavilla A., de Fabritiis C.
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Spherical Coefficients of Slice Regular Functions [PDF]
Results in Mathematics, 2021 AbstractGiven a quaternionic slice regular function f, we give a direct and effective way to compute the coefficients of its spherical expansion at any point. Such coefficients are obtained in terms of spherical and slice derivatives of the function itself. Afterwards, we compare the coefficients of f with those of its slice derivative $$\partial _{c}f$
amedeo altavilla
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$*$-logarithm for slice regular functions
Rendiconti Lincei, Matematica e Applicazioni, 2023 In this paper, we study the (possible) solutions of the equation \exp_*(f)=g , where g is a slice regular never vanishing function on a circular domain of the ...
Amedeo Altavilla, Chiara de Fabritiis
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The Bohr Theorem for slice regular functions [PDF]
Mathematische Nachrichten, 2012 AbstractIn this paper we prove the Bohr Theorem for slice regular functions. Following the historical path that led to the proof of the classical Bohr Theorem, we also extend the Borel‐Carathéodory Theorem to the new setting.
Della Rocchetta, Chiara +2 more
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Twistor interpretation of slice regular functions [PDF]
Journal of Geometry and Physics, 2018 Given a slice regular function $f:Ω\subset\mathbb{H}\to \mathbb{H}$, with $Ω\cap\mathbb{R}\neq \emptyset$, it is possible to lift it to a surface in the twistor space $\mathbb{CP}^{3}$ of $\mathbb{S}^4\simeq \mathbb{H}\cup \{\infty\}$ (see~\cite{gensalsto}).
Amedeo Altavilla, Altavilla A.
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Fractional Slice Regular Functions of a Quaternionic Variable
Results in Mathematics, 2023 The theory of slice regular functions of a quaternionic variable on the unit ball of the quaternions was introduced by Gentili and Struppa in 2006 and nowadays it is a well established function theory, especially in view of its applications to operator theory.
José Oscar González-Cervantes +2 more
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Slice regular functions in several variables
Mathematische Zeitschrift, 2022 AbstractIn this paper, we lay the foundations of the theory of slice regular functions in several (non-commuting) variables ranging in any real alternative $$^*$$ ∗ -algebra, including quaternions, octonions and Clifford algebras.
Perotti, Alessandro, Ghiloni, Riccardo
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The argument principle for quaternionic slice regular functions [PDF]
Michigan Mathematical Journal, 2011 The paper is devoted to special aspects of slice regular functions. For this type of functions the Cullen derivative is well-defined. Quaternionic (one-sided) power series and a corresponding Cauchy product is defined. Zeros of such functions only consist of isolated points and 2-spheres.
Fabio Vlacci, VLACCI, FABIO
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Invariants and automorphisms for slice regular functions
Journal of Noncommutative GeometryLet A be one of the following Clifford algebras: \mathbb{R}_{2} \cong \mathbb{H} or \mathbb{R}_{3}
Cinzia Bisi, Jörg Winkelmann
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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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