The Spherical $π$-Operator

Details The Spherical $π$-Operator The Spherical $π$-Operator

2008-11-20

arxiv.org/abs/0811.3257v1

Mathematics

Classical Analysis and ODEs

This is a 21 page manuscript on the spherical $\pi$-operator defined over domains in the standard $(n-1)$-D unit sphere $S^(n-

Scientific paper

In this article, we define the spherical $\pi$-operator over domains in the $(n-1)$-D unit sphere $S^n$ of $R^n$ and develop new and analogous results on the operator it self and its mapping properties. We introduce the spherical Dirac operator $\Gamma_\alpha$ as an $\alpha$- shift of of $\Gamma_omega$, where $\Gamma_omega$ is the negative of the wedge (or Grassmann) product of $\omega$ with that of the Dirac operator $D_\omega$. A gegenbauer polynomial is used as a Cauchy kernel for the spherical Dirac operator $\Gamma_alpha$.

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