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http://hdl.handle.net/10773/16925
Título: | Fischer Decomposition and Cauchy-Kovalevskaya extension in fractional Clifford analysis: the Riemann-Liouville case |
Autor: | Vieira, N. |
Palavras-chave: | Fractional monogenic polynomials Fischer decomposition Almansi decomposition Cauchy-Kovalevskaya extension theorem Fractional Clifford analysis Fractional Dirac operator Riemann-Liouville derivatives |
Data: | Fev-2017 |
Editora: | Cambridge University Press |
Resumo: | 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 |
URI: | http://hdl.handle.net/10773/16925 |
DOI: | 10.1017/S0013091516000109 |
ISSN: | 0013-0915 |
Aparece nas coleções: | CIDMA - Artigos CHAG - Artigos |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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artigo33_VF.pdf | Documento Principal | 415.89 kB | Adobe PDF | Ver/Abrir |
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