Search Results - Functions of hypercomplex variables

Discrete pseudo‐differential operators in hypercomplex analysis by Cerejeiras, Paula, Kaehler, Uwe, Lucas, Simão

“…In this paper we discuss discrete pseudo‐differential operators in the context of hypercomplex analysis…”
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A new theory of regular functions of a quaternionic variable by 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…”
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Slice regular functions in several variables by Ghiloni, Riccardo, Perotti, Alessandro

“… This higher dimensional function theory is an extension of the classical theory of holomorphic functions of several complex variables…”
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Extension results for slice regular functions of a quaternionic variable by 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…”
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On the generators of Clifford semigroups: Polynomial resolvents and their integral transforms by 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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Twistor interpretation of slice regular functions by 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…”
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Powers of Elliptic Scator Numbers by Fernandez-Guasti, Manuel

“… + 1 dimensions, when the real part and any one hypercomplex component are considered…”
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Slice-by-slice and global smoothness of slice regular and polyanalytic functions by 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. Let Ω ⊂ H be a domain, i.e…”
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Roots of Elliptic Scator Numbers by 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 by Grigor'ev, Yu. M.

“…Unlike in complex analysis, in all hypercomplex function theories a hypercomplex variable is not monogenic (regular…”
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Laguerre derivative and monogenic Laguerre polynomials: An operational approach by 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 of Clifford Analysis as a refinement…”
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Monogenic pseudo-complex power functions and their applications by 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 the solution of different concrete problems…”
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Hypercomplex derivative bases of polynomials in Clifford analysis by Aloui, L., Hassan, G. F.

“…Convergence properties of hypercomplex derivative bases of special monogenic polynomials are studied…”
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Regular functions on a Clifford algebra by Gentili, Graziano, Struppa, Daniele C.

“…In [Gentili, G. and Stoppato, C., 2007, Zeros of regular functions and polynomials of a quaternionic variable, n. 1…”
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On a spatial generalization of the Kolosov-Muskhelishvili formulae by 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…”
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Cauchy-Riemann operators and local slice analysis over real alternative algebras by Perotti, Alessandro

“…We prove some formulas relating Cauchy-Riemann operators defined on hypercomplex subspaces of an alternative…”
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Special Functions of Hypercomplex Variable on the Lattice Based on SU(1,1) by Faustino, Nelson

“…Based on the representation of a set of canonical operators on the lattice [...], which are Clifford-vector-valued, we will introduce new families of special functions of hypercomplex variable possessing [...] symmetries…”
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A representation formula for slice regular functions over slice-cones in several variables by Dou, Xinyuan, Ren, Guangbin, Sabadini, Irene

“… cone. Slice regular functions can be defined on open sets in τ s , W C d and a number of results can be proved in this framework, among which a representation formula…”
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Commutative hypercomplex numbers and functions of hypercomplex variable: a matrix study by Catoni, Francesco, Cannata, Roberto, Nichelatti, Enrico, Zampetti, Paolo

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Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions by 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…”
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