论文标题
pizzetti公式和球体上的ra rad ra
Pizzetti formulae and the Radon Transform on the Sphere
论文作者
论文摘要
在本文中，我们在$ \ mathbb {r}^m $的单位球体$ \ mathbb {s}^{m-1} $上获取Pizzetti-Type公式，并研究其应用程序，以使球形rad radon变换颠倒。特别是，我们在$（m-2）$ - $ \ mathbb {s}^{m-1} $，$（M-1）$ - 尺寸尺寸子球和$（M-1）$ - 尺寸的球形帽以上，作为合适的Delta分布的作用，以$ \ MATHBB {S}^{M-1} $，$（M-1）$ - 尺寸的集成来进行集成。反过来，这导致了pizzetti公式，这些公式在So $（M-1）$ - 不变的差分运算符方面表达了这种积分。在本文的最后一部分中，我们使用其中一些表达式来推导radon transformulas $ \ mathbb {s}^{m-1} $以直接方式推导。
In this paper, we obtain Pizzetti-type formulae on regions of the the unit sphere $\mathbb{S}^{m-1}$ of $\mathbb{R}^m$, and study their applications to the problem of inverting the spherical Radon transform. In particular, we approach integration over $(m-2)$-dimensional sub-spheres of $\mathbb{S}^{m-1}$, $(m-1)$-dimensional sub-balls, and over $(m-1)$-dimensional spherical caps as the action of suitable concentrated delta distributions. In turn, this leads to Pizzetti formulae that express such integrals in terms of the action of SO$(m-1)$-invariant differential operators. In the last section of the paper, we use some of these expressions to derive the inversion formulae for the Radon transform on $\mathbb{S}^{m-1}$ in a direct way.
