Search Results - "Functions of a hypercomplex variable"

Slice regular functions on real alternative algebras by Ghiloni, R., Perotti, A.

“…In this paper we develop a theory of slice regular functions on a real alternative algebra A. Our approach is based on a well-known Fueter's construction. Two…”
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A unified notion of regularity in one hypercomplex variable by Ghiloni, Riccardo, Stoppato, Caterina

“…We define a very general notion of regularity for functions taking values in an alternative real ⁎-algebra. Over Clifford numbers, this notion subsumes the…”
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On the Fueter–Sce theorem for generalized partial-slice monogenic functions by Xu, Zhenghua, Sabadini, Irene

“…In a recent paper, we introduced the concept of generalized partial-slice monogenic functions. The class of these functions includes both monogenic functions…”
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A new series expansion for slice regular functions by Stoppato, Caterina

“…A promising theory of quaternion-valued functions of one quaternionic variable, now called slice regular functions, has been introduced by Gentili and Struppa…”
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Partial slice regularity and Fueter's theorem in several quaternionic variables by Binosi, Giulio

“…We extend some definitions and give new results about the theory of slice analysis in several quaternionic variables. The sets of slice functions that are…”
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A Survey on Quasiconformal Functions with Application to the Case of Functions of a Hypercomplex Variable by Vlacci, Fabio

“…The notion (but not the name) of a quasiconformal mapping was first introduced by H. Grötzsch in 1928. He was mainly interested in transformations of the plane…”
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Generalized Partial-Slice Monogenic Functions: A Synthesis of Two Function Theories by Xu, Zhenghua, Sabadini, Irene

“…In this paper, we review the notion of generalized partial-slice monogenic functions that was introduced by the authors in Xu and Sabadini (Generalized…”
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A unified theory of regular functions of a hypercomplex variable by Ghiloni, Riccardo, Stoppato, Caterina

“…This work proposes a unified theory of regularity in one hypercomplex variable: the theory of \(T\)-regular functions. In the special case of quaternion-valued…”
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Global differential equations for slice regular functions by Ghiloni, Riccardo, Perotti, Alessandro

“…In the present paper, we give a system of global differential equations which are satisfied by slice regular functions on a real alternative algebra. By means…”
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Noncommutative Cauchy Integral Formula by Ghiloni, Riccardo, Perotti, Alessandro, Recupero, Vincenzo

“…The aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for C 1 functions on a real alternative…”
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Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect by Ghiloni, R., Perotti, A.

“…We study in detail the zero set of a slice regular function of a quaternionic or octonionic variable. By means of a division lemma for convergent power series,…”
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Some properties for quaternionic slice regular functions on domains without real points by Altavilla, Amedeo

“…The theory of slice regular functions over the quaternions, introduced by Gentili and Struppa in 2007, was born on balls centred in the origin and has been…”
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A Bianchi’s Relation Between Commutative Hypercomplex Numbers and Riemannian Geometry: an Updated Reading by Catoni, Francesco

“…). After summarizing this paper we take into account the developments from the time of publication, in particular the formalization of the theory of functions of a hypercomplex variable that allows us…”
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A Phragmén - Lindelöf principle for slice regular functions by Gentili, G, Stoppato, C, Struppa, D C

“… 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 equations…”
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Estimation of parameters and recognition of images of three-dimensional objects with disordered samples by Rozhentsov, A. A., Baev, A. A., Naumov, A. S.

“… The approach is based on obtaining a secondary analytical description of an object in the form of a polynomial function of a hypercomplex variable that projects samples of the object surface onto a sphere…”
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The application of biquaternion analysis to the transformation of the electromagnetic field and geometrical optics by Sullivan, Christopher Charles

“…The addition of the laws of reflection and refraction to basic Euclidean geometry gives rise to an optical geometry which extends into non-Euclidean spaces…”
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The application of biquaternion analysis to the transformation of the electromagnetic field and geometrical optics by Sullivan, Christopher Charles

“…The addition of the laws of reflection and refraction to basic Euclidean geometry gives rise to an optical geometry which extends into non-Euclidean spaces…”
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On a Criterion of Local Invertibility and Conformality for Slice Regular Quaternionic Functions by Gori, Anna, Vlacci, Fabio

“…A new criterion for local invertibility of slice regular quaternionic functions is obtained. This paper is motivated by the need to find a geometrical…”
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