scholarly journals Fischer decomposition for osp(4|2)-monogenics in quaternionic Clifford analysis

2016 ◽  
Vol 39 (16) ◽  
pp. 4874-4891 ◽  
Author(s):  
Fred Brackx ◽  
Hennie De Schepper ◽  
David Eelbode ◽  
Roman Lávička ◽  
Vladimir Souček
Keyword(s):  
Clifford Analysis ◽  
Fischer Decomposition ◽  
Quaternionic Clifford Analysis

Quaternionic Clifford Analysis: The Hermitian Setting

2007 ◽  
Vol 1 (1) ◽  
pp. 97-113 ◽  
Author(s):  
Dixan Peña-Peña ◽  
Irene Sabadini ◽  
Frank Sommen
Keyword(s):  
Clifford Analysis ◽  
Quaternionic Clifford Analysis

scholarly journals Fischer Decomposition in Generalized Fractional Ternary Clifford Analysis

2017 ◽  
Vol 11 (5) ◽  
pp. 1077-1093 ◽  
Author(s):  
P. Cerejeiras ◽  
A. Fonseca ◽  
M. Vajiac ◽  
N. Vieira
Keyword(s):  
Clifford Analysis ◽  
Fischer Decomposition

Fundaments of Quaternionic Clifford Analysis I: Quaternionic Structure

2014 ◽  
Vol 24 (4) ◽  
pp. 955-980 ◽  
Author(s):  
F. Brackx ◽  
H. De Schepper ◽  
D. Eelbode ◽  
R. Lávička ◽  
V. Souček
Keyword(s):  
Clifford Analysis ◽  
Quaternionic Structure ◽  
Quaternionic Clifford Analysis

scholarly journals Fischer Decomposition and Cauchy–Kovalevskaya Extension in Fractional Clifford Analysis: The Riemann–Liouville Case

2016 ◽  
Vol 60 (1) ◽  
pp. 251-272 ◽  
Author(s):  
N. Vieira
Keyword(s):  
Clifford Analysis ◽  
Extension Theorem ◽  
Extension Principle ◽  
Homogeneous Polynomials ◽  
Fischer Decomposition ◽  
Spherical Monogenics ◽  
Fueter Polynomials ◽  
Fractional Clifford Analysis ◽  
Extension Of Functions ◽  
Fractional Function

AbstractIn this paper we present the basic tools of a fractional function theory in higher dimensions by means of a fractional correspondence to the Weyl relations via fractional Riemann–Liouville derivatives. A Fischer decomposition, Almansi decomposition, fractional Euler and Gamma operators, monogenic projection, and basic fractional homogeneous powers are constructed. Moreover, we establish the fractional Cauchy–Kovalevskaya extension (FCK extension) theorem for fractional monogenic functions defined on ℝd. Based on this extension principle, fractional Fueter polynomials, forming a basis of the space of fractional spherical monogenics, i.e. fractional homogeneous polynomials, are introduced. We study the connection between the FCK extension of functions of the form xPl and the classical Gegenbauer polynomials. Finally, we present an example of an FCK extension.

On a Mixed Fischer Decomposition in Clifford Analysis

2016 ◽  
Vol 11 (2) ◽  
pp. 359-374
Author(s):  
Juan Bory Reyes ◽  
Hennie De Schepper ◽  
Alí Guzmán Adán ◽  
Frank Sommen
Keyword(s):  
Clifford Analysis ◽  
Fischer Decomposition

scholarly journals Fundaments of quaternionic Clifford analysis II: splitting of equations

2016 ◽  
Vol 62 (5) ◽  
pp. 616-641 ◽  
Author(s):  
F. Brackx ◽  
H. De Schepper ◽  
D. Eelbode ◽  
R. Lávička ◽  
V. Souček
Keyword(s):  
Clifford Analysis ◽  
Quaternionic Clifford Analysis

scholarly journals Matrix Cauchy and Hilbert transforms in Hermitian quaternionic Clifford analysis

2013 ◽  
Vol 58 (8) ◽  
pp. 1057-1069 ◽  
Author(s):  
Ricardo Abreu-Blaya ◽  
Juan Bory-Reyes ◽  
Fred Brackx ◽  
Hennie De Schepper ◽  
Frank Sommen
Keyword(s):  
Clifford Analysis ◽  
Hilbert Transforms ◽  
Quaternionic Clifford Analysis
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