论文标题
关于移动的放克 - 拉登变换和相关谐波分析的注入性
On the Injectivity of the Shifted Funk-Radon Transform and Related Harmonic Analysis
论文作者
论文摘要
获得了必要和足够的条件，以与$ k $二维完全Geodesic Submanifolds相关的移动的Funk-Radon变换获得了单位球的$ s^n $ in $ \ MATHBB {r}^{n+1} $。该结果概括了$ s^n $的球形手段的众所周知的陈述，并根据jacobi多项式的零来制定。相关的谐波分析是开发的，包括诱发的Stiefel（或Grassmannian）谐波，Funk-Hecke型定理，加法公式和乘数的新概念。讨论了一些观点和猜想。
Necessary and sufficient conditions are obtained for injectivity of the shifted Funk-Radon transform associated with $k$-dimensional totally geodesic submanifolds of the unit sphere $S^n$ in $\mathbb{R}^{n+1}$. This result generalizes the well known statement for the spherical means on $S^n$ and is formulated in terms of zeros of Jacobi polynomials. The relevant harmonic analysis is developed, including a new concept of induced Stiefel (or Grassmannian) harmonics, the Funk-Hecke type theorems, addition formula, and multipliers. Some perspectives and conjectures are discussed.
