Fischer decomposition for spinor valued polynomials in several variables

Roman Lavicka; Vladimir Soucek

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arXiv · 1708.01426

Fischer decomposition for spinor valued polynomials in several variables

Roman Lavicka·Vladimir Soucek

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Abstract

It is well-known that polynomials decompose into spherical harmonics. This result is called separation of variables or the Fischer decomposition. In the paper we prove the Fischer decomposition for spinor valued polynomials in $k$ vector variables of ${\mathbb R}^m$ under the stable range condition $m\geq 2k$. Here the role of spherical harmonics is played by monogenic polynomials, that is, polynomial solutions of the Dirac equation in $k$ vector variables.

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Roman Lavicka, Vladimir Soucek. 2017-08-04. Fischer decomposition for spinor valued polynomials in several variables. https://arxiv.org/abs/1708.01426

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