scholarly journals Gelfand–Tsetlin bases for spherical monogenics in dimension 3

2012 ◽  
Vol 28 (4) ◽  
pp. 1165-1192 ◽  
Author(s):  
Sebastian Bock ◽  
Klaus Gürlebeck ◽  
Roman Lávička ◽  
Vladimír Souček
Keyword(s):  
Spherical Monogenics

scholarly journals Orthogonal basis for spherical monogenics by step two branching

2011 ◽  
Vol 41 (2) ◽  
pp. 161-186 ◽  
Author(s):  
R. Lávička ◽  
V. Souček ◽  
P. Van Lancker
Keyword(s):  
Orthogonal Basis ◽  
Spherical Monogenics

On an Orthonormal Basis of Solid Spherical Monogenics Recursively Generated by Anti-Holomorphic z̄-Powers

2009 ◽  
Author(s):  
S. Bock ◽  
K. Gürlebeck ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Orthonormal Basis ◽  
Spherical Monogenics

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 Generating Functions for Spherical Harmonics and Spherical Monogenics

2014 ◽  
Vol 24 (4) ◽  
pp. 995-1004 ◽  
Author(s):  
P. Cerejeiras ◽  
U. Kähler ◽  
R. Lávička
Keyword(s):  
Spherical Harmonics ◽  
Generating Functions ◽  
Spherical Monogenics

scholarly journals The inverse Fueter mapping theorem in integral form using spherical monogenics

2012 ◽  
Vol 194 (1) ◽  
pp. 485-505 ◽  
Author(s):  
Fabrizio Colombo ◽  
Irene Sabadini ◽  
Franciscus Sommen
Keyword(s):  
Integral Form ◽  
Spherical Monogenics
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