scholarly journals The Cauchy-Kovalevskaya extension theorem in discrete Clifford analysis

2011 ◽  
Vol 10 (4) ◽  
pp. 1097-1109 ◽  
Author(s):  
Hilde De Ridder ◽  
Hennie Schepper ◽  
Frank Sommen
Keyword(s):  
Clifford Analysis ◽  
Extension Theorem ◽  
Discrete Clifford Analysis

scholarly journals The Cauchy-Kovalevskaya Extension Theorem in Discrete Clifford Analysis

2010 ◽  
Author(s):  
H. De Ridder ◽  
H. De Schepper ◽  
F. Sommen ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Clifford Analysis ◽  
Extension Theorem ◽  
Discrete Clifford Analysis

scholarly journals Spinor Spaces in Discrete Clifford Analysis

2017 ◽  
Vol 11 (5) ◽  
pp. 1113-1137
Author(s):  
H. De Ridder ◽  
T. Raeymaekers
Keyword(s):  
Clifford Analysis ◽  
Discrete Clifford Analysis

scholarly journals The Cauchy–Kovalevskaya extension theorem in Hermitian Clifford analysis

2011 ◽  
Vol 381 (2) ◽  
pp. 649-660 ◽  
Author(s):  
F. Brackx ◽  
H. De Schepper ◽  
R. Lávička ◽  
V. Souček
Keyword(s):  
Clifford Analysis ◽  
Extension Theorem ◽  
Hermitian Clifford Analysis

Discrete Clifford analysis: the one-dimensional setting

2012 ◽  
Vol 57 (7-8) ◽  
pp. 903-920 ◽  
Author(s):  
H. De Bie ◽  
H. De Ridder ◽  
F. Sommen
Keyword(s):  
Clifford Analysis ◽  
One Dimensional ◽  
Discrete Clifford Analysis ◽  
The One

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.

scholarly journals A Basic Framework for Discrete Clifford Analysis

2009 ◽  
Vol 18 (4) ◽  
pp. 385-395 ◽  
Author(s):  
Hennie De Schepper ◽  
Frank Sommen ◽  
Liesbet Van de Voorde
Keyword(s):  
Clifford Analysis ◽  
Basic Framework ◽  
Discrete Clifford Analysis

scholarly journals Taylor Series Expansion in Discrete Clifford Analysis

2013 ◽  
Vol 8 (2) ◽  
pp. 485-511 ◽  
Author(s):  
Hilde De Ridder ◽  
Hennie De Schepper ◽  
Frank Sommen
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Clifford Analysis ◽  
Taylor Series Expansion ◽  
Discrete Clifford Analysis

scholarly journals Discrete Clifford Analysis

2014 ◽  
pp. 1-19
Author(s):  
Uwe Kaehler ◽  
Frank Sommen
Keyword(s):  
Clifford Analysis ◽  
Discrete Clifford Analysis
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