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Cauchy–Kovalevskaya Extension Theorem in Fractional Clifford Analysis

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Abstract

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.

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Acknowledgments

N. Vieira was supported by Portuguese funds through the CIDMA—Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT—Fundação para a Ciência e a Tecnologia”), within project PEst-OE/MAT/UI4106/2014.

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  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

    N. Vieira

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  1. N. Vieira
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Correspondence to N. Vieira.

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Communicated by Fabrizio Colombo.

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Vieira, N. Cauchy–Kovalevskaya Extension Theorem in Fractional Clifford Analysis. Complex Anal. Oper. Theory 9, 1089–1109 (2015). https://doi.org/10.1007/s11785-014-0395-x

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