Search Results - Functions of hypercomplex variables and generalized 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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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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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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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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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…”
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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…”
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Generalized Bohr radius for slice regular functions over quaternions by Xu, Zhenghua

“… To be precise, two results of Enrico Bombieri are generalized by means of a new idea into the class of slice regular functions over quaternions…”
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Hypercomplex Fock states for discrete electromagnetic Schrödinger operators: A Bayesian probability perspective by Faustino, N.

“… Schrödinger operators from a multivector calculus perspective. This naturally lead to hypercomplex versions of Poisson…”
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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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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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Characterizations of Herglotz–Nevanlinna Functions Using Positive Semi-Definite Functions and the Nevanlinna Kernel in Several Variables by Nedic, Mitja

“… This allows us to propose a multidimensional analogue of the classical Nevanlinna kernel and a definition of generalized Nevanlinna functions in several variables…”
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A note on a generalized Joukowski transformation by Malonek, H.R., De Almeida, R.

“… ≥ 2 , an n -dimensional hypercomplex analogue of the Joukowski transformation and describe in some detail the 3D case…”
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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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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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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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Generalized Bernoulli Numbers and Polynomials in the Context of the Clifford Analysis by Sreelatha, Chandragiri, Olga A., Shishkina

“…In this paper, we consider the generalization of the Bernoulli numbers and polynomials for the case of the hypercomplex variables…”
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Feedforward–Feedback Controller Based on a Trained Quaternion Neural Network Using a Generalised HR Calculus with Application to Trajectory Control of a Three-Link Robot Manipulator by Takahashi, Kazuhiko, Tano, Eri, Hashimoto, Masafumi

“… This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function concerning quaternion variables and designs a feedback…”
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Feedforward–Feedback Controller Based on a Trained Quaternion Neural Network Using a Generalised Calculus with Application to Trajectory Control of a Three-Link Robot Manipulator by Kazuhiko Takahashi, Eri Tano, Masafumi Hashimoto

“… This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function concerning quaternion variables and designs a feedback…”
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Slice Spirallike Functions over Quaternions by Xu, Zhenghua, Zhang, Die, Liu, Yuan, Si, Jiajia

“…In this paper, we study the analogue of spirallikeness for slice regular functions of one quaternionic variable…”
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Analytical Solutions for Generalized Stochastic HSC-KdV Equations with Variable Coefficients Using Hermite Transform and F-Expansion Method by Zakarya, Mohammed, Al-Shehri, Nadiah Zafer, Ali, Hegagi M., Abd-Rabo, Mahmoud A., Rezk, Haytham M.

“…This study focuses on analyzing the generalized HSC-KdV equations characterized by variable coefficients and Wick-type stochastic (Wt.S) elements…”
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