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Title: Fischer Decomposition and Cauchy-Kovalevskaya extension in fractional Clifford analysis: the Riemann-Liouville case
Author: Vieira, N.
Keywords: Fractional monogenic polynomials
Fischer decomposition
Almansi decomposition
Cauchy-Kovalevskaya extension theorem
Fractional Clifford analysis
Fractional Dirac operator
Riemann-Liouville derivatives
Issue Date: Feb-2017
Publisher: Cambridge University Press
Abstract: In 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 will be constructed. Moreover, we establish the fractional Cauchy-Kovalevskaya extension ($FCK$-extension) theorem for fractional monogenic functions defined on $\BR^d$. 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 studied the connection between the $FCK$-extension of functions of the form $\x ~P_l$ and the classical Gegenbauer polynomials. Finally we present an example of an $FCK$-extension.
Peer review: yes
DOI: 10.1017/S0013091516000109
ISSN: 0013-0915
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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