Výsledky vyhledávání - "Functions of hypercomplex variable"

Cauchy-Riemann operators and local slice analysis over real alternative algebras Autor Perotti, Alessandro

“…We prove some formulas relating Cauchy-Riemann operators defined on hypercomplex subspaces of an alternative *-algebra to a differential operator associated…”
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A representation formula for slice regular functions over slice-cones in several variables Autor Dou, Xinyuan, Ren, Guangbin, Sabadini, Irene

“…The aim of this paper is to extend the so called slice analysis to a general case in which the codomain is a real vector space of even dimension, i.e. is of…”
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Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions Autor Dou, Xinyuan, Ren, Guangbin, Sabadini, Irene, Yang, Ting

“…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…”
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On a factorization of the Schrödinger and Klein-Gordon operators Autor Cerejeiras, Paula, Kähler, Uwe, Kravchenko, Vladislav V.

“…A general scheme for factorizing second‐order time‐dependent operators of mathematical physics is given, which allows a reduction of corresponding second‐order…”
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A Bianchi’s Relation Between Commutative Hypercomplex Numbers and Riemannian Geometry: an Updated Reading Autor Catoni, Francesco

“… In a paper published in 1916, the mathematician L. Bianchi has shown that the commutative hypercomplex numbers can be related with Riemannian spaces with…”
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A new theory of regular functions of a quaternionic variable Autor Gentili, Graziano, Struppa, Daniele C.

“…In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows…”
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On the generators of Clifford semigroups: Polynomial resolvents and their integral transforms Autor Ghiloni, Riccardo, Recupero, Vincenzo

“…This paper deals with generators A of strongly continuous right linear semigroups in Banach two-sided spaces whose set of scalars is an arbitrary Clifford…”
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Extension results for slice regular functions of a quaternionic variable Autor Colombo, Fabrizio, Gentili, Graziano, Sabadini, Irene, Struppa, Daniele

“…In this paper we prove a new Representation Formula for slice regular functions, which shows that the value of a slice regular function f at a point q = x + y…”
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Slice regular functions in several variables Autor Ghiloni, Riccardo, Perotti, Alessandro

“…In this paper, we lay the foundations of the theory of slice regular functions in several (non-commuting) variables ranging in any real alternative ∗ -algebra,…”
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Discrete pseudo‐differential operators in hypercomplex analysis Autor Cerejeiras, Paula, Kaehler, Uwe, Lucas, Simão

“…In this paper we discuss discrete pseudo‐differential operators in the context of hypercomplex analysis. We will provide the definitions and establish the…”
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Twistor interpretation of slice regular functions Autor Altavilla, Amedeo

“…Given a slice regular function f:Ω⊂H→H, with Ω∩R≠∅, it is possible to lift it to surfaces in the twistor space CP3 of S4≃H∪{∞} (see Gentili et al., 2014). In…”
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Powers of Elliptic Scator Numbers Autor Fernandez-Guasti, Manuel

“…Elliptic scator algebra is possible in 1+n dimensions, n∈N. It is isomorphic to complex algebra in 1 + 1 dimensions, when the real part and any one…”
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Slice-by-slice and global smoothness of slice regular and polyanalytic functions Autor Ghiloni, Riccardo

“…The concept of slice regular function over the real algebra H of quaternions is a generalization of the notion of holomorphic function of a complex variable…”
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Roots of Elliptic Scator Numbers Autor Fernandez-Guasti, Manuel

“…The Victoria equation, a generalization of De Moivre’s formula in 1+n dimensional scator algebra, is inverted to obtain the roots of a scator. For the qth root…”
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Regular quaternionic polynomials and their properties Autor Grigor'ev, Yu. M.

“…Unlike in complex analysis, in all hypercomplex function theories a hypercomplex variable is not monogenic (regular) and there exists a problem to define…”
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Laguerre derivative and monogenic Laguerre polynomials: An operational approach Autor Cação, I., Falcão, M.I., Malonek, H.R.

“…Hypercomplex function theory generalizes the theory of holomorphic functions of one complex variable by using Clifford Algebras and provides the fundamentals…”
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Monogenic pseudo-complex power functions and their applications Autor Cruz, Carla, Irene Falcão, Maria, Malonek, Helmuth R.

“…The use of a non‐commutative algebra in hypercomplex function theory requires a large variety of different representations of polynomials suitably adapted to…”
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Regular functions on a Clifford algebra Autor Gentili, Graziano, Struppa, Daniele C.

“…In [Gentili, G. and Stoppato, C., 2007, Zeros of regular functions and polynomials of a quaternionic variable, n. 1 (Dipartimento di Matematica "U. Dini",…”
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On a spatial generalization of the Kolosov-Muskhelishvili formulae Autor Bock, S., Gürlebeck, K.

“…The main goal of this paper is to construct a spatial analog to the Kolosov–Muskhelishvili formulae using the framework of the hypercomplex function theory. We…”
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Hypercomplex derivative bases of polynomials in Clifford analysis Autor Aloui, L., Hassan, G. F.

“…Convergence properties of hypercomplex derivative bases of special monogenic polynomials are studied. These new results extend and improve a lot of known works…”
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