Cauchy–Kovalevskaya Extension Theorem in Fractional Clifford Analysis

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• 作者：N. Vieira
• 关键词：Cauchy–Kovalevskaya extension theorem ; Fractional Clifford analysis ; Fractional monogenic polynomials ; Fractional Dirac operator ; Caputo derivatives ; Primary 30G35 ; Secondary 35A10 ; 26A33 ; 30A05 ; 31B05
• 刊名：Complex Analysis and Operator Theory
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：9
• 期：5
• 页码：1089-1109
• 全文大小：503 KB
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  7.De Ridder, H.: Discrete Clifford analysis: function theory and integral transforms. PhD Thesis, University of Gent (2013)
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  14.Li, M.F., Ren, J.R., Zhu, T.: Fractional Vector Calculus and Fractional Special Function (2010). arXiv:-001.-889v1
  15.Malonek, H., Pe?a-Pe?a, D., Sommen, F.: A Cauchy–Kowalevski theorem for inframonogenic functions. Math. J. Okayama Univ. 53, 167-72 (2011)MATH MathSciNet
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• 作者单位：N. Vieira (1)
  
  1. Department of Mathematics, CIDMA, Center for Research and Development in Mathematics and Applications, University of Aveiro, Campus Universitário de Santiago, 3810-193?, Aveiro, Portugal
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Operator Theory
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1661-8262

文摘

In this paper, we establish the fractional Cauchy–Kovalevskaya extension (\(\textit{FCK}\)-extension) theorem for fractional monogenic functions defined on \(\mathbb {R}^d\). 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 \(\textit{FCK}\)-extension of functions of the form \(x^\alpha P_l\) and the classical Gegenbauer polynomials. Finally we present two examples of \(\textit{FCK}\)-extension.