scholarly journals Fischer Decomposition in Generalized Fractional Clifford Analysis

2017 ◽  
pp. 37-53
Author(s):  
P. Cerejeiras ◽  
A. Fonseca ◽  
U. Kähler ◽  
N. Vieira
Keyword(s):  
Clifford Analysis ◽  
Fischer Decomposition ◽  
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.

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

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 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

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
Sign in / Sign up

Export Citation Format

Share Document