In this paper, we study a refinement of the Szegö-Radon transform in the hypermonogenic setting. Hypermonogenic functions form a subclass of monogenic functions arising in the study of a modified Dirac operator, which allows for weaker symmetries and also has a strong connection to the hyperbolic metric. In particular, we construct a projection operator from a module of hypermonogenic functions in ${\mathbb{R}}^{p+q}$ onto a suitable submodule of plane waves parameterized by a vector on the unit sphere of ${\mathbb{R}}^q$. Moreover, we study the interaction of this Szegö-Radon transform with the generalized Cauchy-Kovalevskaya extension operator. Finally, we develop a reconstruction (inversion) method for this transform.

在本文中，我们研究了超单基因环境中 Szegö-Radon 变换的改进。Hypermonogenic 函数形成了研究修改后的 Dirac 算子时出现的单基因函数的一个子类，它允许较弱的对称性，并且与双曲线度量有很强的联系。特别地，我们从一个超单基因函数模块构建了一个投影算子${\mathbb{电阻}}^{磷+q}$ 到由单位球面上的向量参数化的平面波的合适子模块 ${\mathbb{电阻}}^q$. 此外，我们研究了这种 Szegö-Radon 变换与广义 Cauchy-Kovalevskaya 扩展算子的相互作用。最后，我们为这种变换开发了一种重建（反演）方法。