关于球面单演函数的博克纳公式

Bochner’s formula for spherical monogenics

在克里佛德分析的框架下,研究了L2(Rd;Cl0,d)空间的直和分解,使得每个子空间在一种广义傅里叶变换下是保持不变的,这种广义傅里叶变换称为克里佛德-傅里叶变换.同时,还得到了L2(Rd;Cl0,d)的每个子空间中函数克里佛德-傅里叶变换的具体表达式,这推广了经典的球面单演函数的博克纳(Bochner)公式.

In the framework of Clifford analysis, we study the counterpart of a direct sum decomposition of L2(?d;Cl0,d) into subspaces which are invariant under a generalized Fourier transform, which is called Clifford-Fourier transform in the literature. The explicit Clifford-Fourier transform formula for each component of a function in L2(?d;Cl0,d) is established, which generalizes the Bochner’s formula for spherical monogenics.