Fractional Clifford Analysis

2013 ◽  
pp. 191-201 ◽  
Author(s):  
Uwe Kähler ◽  
Nelson Vieira
Keyword(s):  
Clifford Analysis ◽  
Fractional 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 generalized Hilbert transforms and their interaction with the Radon transform in Clifford analysis

2007 ◽  
Vol 30 (9) ◽  
pp. 1071-1092 ◽  
Author(s):  
Fred Brackx ◽  
Bram De Knock ◽  
Hennie De Schepper
Keyword(s):  
Radon Transform ◽  
Clifford Analysis ◽  
Hilbert Transforms

Eigenvalue problems in the framework of Clifford analysis

2001 ◽  
Vol 11 (S2) ◽  
pp. 301-316 ◽  
Author(s):  
Wolfgang Sprößig
Keyword(s):  
Clifford Analysis ◽  
Eigenvalue Problems

scholarly journals Numerical Clifford analysis for nonlinear Schrödinger problem

2008 ◽  
Vol 24 (4) ◽  
pp. 1181-1202 ◽  
Author(s):  
P. Cerejeiras ◽  
N. Faustino ◽  
N. Vieira
Keyword(s):  
Clifford Analysis ◽  
Nonlinear Schrödinger

The Hermitian Clifford Analysis Toolbox

2008 ◽  
Vol 18 (3-4) ◽  
pp. 451-487 ◽  
Author(s):  
Fred Brackx ◽  
Hennie De Schepper ◽  
Frank Sommen
Keyword(s):  
Clifford Analysis ◽  
Hermitian Clifford Analysis
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