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Related papers: On quaternionic functions

200 papers

Some comments are made on the matrices which serve as the basis of a quaternionic algebra. We show that these matrices are related with the quaternionic action of the imaginary units from the left and from the right.

Rings and Algebras · Mathematics 2007-05-23 Gisele Ducati

A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…

Complex Variables · Mathematics 2024-02-14 Michael Parfenov

The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperK\"ahler with Torsion). The…

Metric Geometry · Mathematics 2016-07-08 Semyon Alesker

Experimental results on hadronic structures are discussed in view of our physics understanding. Achievements and challenges are noted.

High Energy Physics - Experiment · Physics 2007-05-23 Martin Erdmann

We compare the behavior of a wave packet in the presence of a complex and a pure quaternionic potential step. This analysis, done for a gaussian convolution function, sheds new light on the possibility to recognize quaternionic deviations…

Mathematical Physics · Physics 2009-11-13 Stefano De Leo , Gisele C. Ducati

In this current article, we introduce the quadruple Shehu transform and its inverse. We also introduce some properties of quadruple Shehu transform. The Convolution theorem and its proof are also discussed. Further, to solve homogeneous and…

General Mathematics · Mathematics 2022-12-01 D. D. Pawar , G. G. Bhuttampalle , S. B. Chavhan , Wagdi F. S. Ahmed , R. D. Kadam

Quaternion analysis is considered in full details where a new analyticity condition in complete analogy to complex analysis is found. The extension to octonions is also worked out.

High Energy Physics - Theory · Physics 2008-02-03 Khaled Abdel-Khalek

Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…

Functional Analysis · Mathematics 2019-02-12 Florian-Horia Vasilescu

We study a new class of functions that arise naturally in quaternionic analysis, we call them "quasi regular functions". Like the well-known quaternionic regular functions, these functions provide representations of the quaternionic…

Representation Theory · Mathematics 2026-01-26 Igor Frenkel , Matvei Libine

In this paper we study left and right n-regular functions that originally were introduced in [FL4]. When n=1, these functions are the usual quaternionic left and right regular functions. We show that n-regular functions satisfy most of the…

Complex Variables · Mathematics 2020-12-01 Igor Frenkel , Matvei Libine

Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.

High Energy Physics - Phenomenology · Physics 2007-05-23 M. Grazzini

In this paper we present a perturbation theory for constant quaternionic potentials. The effects of quaternionic perturbations are explicitly treated for bound states of hydrogen atom, infinite potential well and harmonic oscillator.…

Quantum Physics · Physics 2019-03-20 Stefano De Leo , Gisele Ducati , Caio Almeida Alves de Souza

New definitions of determinant functionals over the quaternion skew field are given in this paper. The inverse matrix over the quaternion skew field is represented by analogues of the classical adjoint matrix. Cramer rule for right and left…

Rings and Algebras · Mathematics 2007-05-23 Ivan Kyrchei

Based on a new generalization of Cauchy-Riemann system presented in this paper, we introduce a class of quaternion-valued functions of a quaternionic variable, which are called algebraic regular functions. The set of algebraic regular…

Complex Variables · Mathematics 2015-11-30 Keqin Liu

The theory of the functional sequences and series is presented; uniformly convergent, convergent in the sense of a mean square and weakly convergent sequences and series are considered. Sequential approach to constructing generalized…

Mathematical Physics · Physics 2011-09-13 Mykhaylo Sukhorolsky

Complex functions have multiple uses in various fields of study, so analyze their characteristics it is of extensive interest to other sciences. This work begins with a particular class of rational functions of a complex variable; over this…

Econometrics · Economics 2019-07-16 Guillermo Daniel Scheidereiter , Omar Roberto Faure

This paper is concerned with the spectral characteristics of quaternionic positive definite functions on the real line. We generalize the Stone's theorem to the case of a right quaternionic linear one-parameter unitary group via two…

Spectral Theory · Mathematics 2024-12-10 Zeping Zhu

In this paper, a new construction of quaternary bent functions from quaternary quadratic forms over Galois rings of characteristic 4 is proposed. Based on this construction, several new classes of quaternary bent functions are obtained, and…

Discrete Mathematics · Computer Science 2013-09-03 Baofeng Wu , Dongdai Lin

Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…

Number Theory · Mathematics 2022-03-01 Joseph Burnett , Alex Taylor

This study examines Quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be…

Quantum Physics · Physics 2016-01-20 Sergio Giardino