Analytic Properties of the Conformal Dirac Operator on the Sphere in Clifford Analysis

2015/05/26 by Brett Pansano, Pansano, Brett
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #math.CV

paper · pdf · doi:10.48550/arxiv.1505.06964

arxiv created 2015/05/26 · openalex publication_date 2015/05/26 · arxiv updated 2015/05/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper the conformal Dirac operator on the sphere is defined to be operating on the space of square-integrable Clifford algebra-valued functions. The spinorial Laplacian of order d>0 is defined and used to establish Sobolev embedding theorems.

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