Fischer decomposition for spinor valued polynomials in several variables
R Lavicka, V Soucek - arXiv preprint arXiv:1708.01426, 2017 - arxiv.org
R Lavicka, V Soucek
arXiv preprint arXiv:1708.01426, 2017•arxiv.orgIt 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.
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.
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 vector variables of under the stable range condition . Here the role of spherical harmonics is played by monogenic polynomials, that is, polynomial solutions of the Dirac equation in vector variables.
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