Some properties and integral transforms in higher spin Clifford analysis

2024/09/16 by Chao Ding, Ding, Chao
Mathematics · Computer Science · #Algebraic and Geometric Analysis #Matrix Theory and Algorithms #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2409.09952

Abstract

Rarita-Schwinger equation plays an important role in theoretical physics. Bure\v s et al. generalized it to arbitrary spin k/2 in 2002 in the context of Clifford algebras. In this article, we introduce the mean value property, Cauchy's estimates, and Liouville's theorem for null solutions to Rarita-Schwinger operator in Euclidean spaces. Further, we investigate boundednesses to the Teodorescu transform and its derivatives. This gives rise to a Hodge decomposition of an L² spaces in terms of the kernel space of the Rarita-Schwinger operator and it also generalizes Bergman spaces in higher spin cases. \endabstract

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