Journal ArticleDOI
A hypercomplex derivative of monogenic functsions in and its Applications
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The authors generalize the definition of a certain derivative of regular functions of variables from the four-dimensional real associative algebra of quaternions to monogenic functions of hypercomplex variables in Rn+1.Abstract:
We generalize the definition of a certain derivative of regular functions of variables from the four-dimensional real associative algebra of quaternions to monogenic functions of hypercomplex variables in Rn+1. Using this concept of derivation we look for primitives of monogenic functions in the set of monogenic functions. The results will be applied for proving a final result about the invertibility of a hypercomplex II-operator.read more
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Proceedings ArticleDOI
Generalized Exponentials through Appell sets in Rn+1 and Bessel functions
Maria Irene Falcão,H. R. Malonek +1 more
TL;DR: In this article, a special class of homogeneous monogenic polynomials constructed in the framework of hypercomplex function theory is presented, in order to be an Appell set of polynomial functions.
Journal ArticleDOI
On a generalized Appell system and monogenic power series
S. Bock,Klaus Gürlebeck +1 more
TL;DR: In this article, a Taylor-type series expansion based on the Appell polynomials is presented, which can be related to the corresponding Fourier series analogously as in the complex one-dimensional case.
Journal ArticleDOI
On Uncertainty Principle for Quaternionic Linear Canonical Transform
TL;DR: In this paper, a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains is established for the quaternionic linear canonical transform (QLCT).
Proceedings ArticleDOI
Special Monogenic Polynomials—Properties and Applications
TL;DR: In this article, a direct and elementary approach to construct a set of homogeneous polynomials involving only products of a hypercomplex variable and its hypercomplex conjugate is presented.
Remarks on the generation of monogenic functions
TL;DR: In this paper, three different methods for generating monogenic functions are considered: Fueter's well known approach to the generation of monogenic quaternion-valued functions by means of holomorphic functions, the solution of hypercomplex differential equations and finally the direct series approach, based on the use of special homogeneous polynomials.
References
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Journal ArticleDOI
Quaternions and matrices of quaternions
TL;DR: A brief survey on quaternions and matrices of quaternion is given in this article, where the authors present new proofs for certain known results and discuss the quaternionic analogues of complex matrices.
Book
Quaternionic analysis and elliptic boundary value problems
TL;DR: In this paper, a generalized version of the LEIBNIZ rule for H-regular functions is presented. But it does not address the problem of boundary value problems of DIRICHLET's type.
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Generalized Exponentials through Appell sets in Rn+1 and Bessel functions
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