论文标题
Euler-Poisson-Darboux方程的逆问题，并移动了$ k $ - 平面变换
The Inverse Problem for the Euler-Poisson-Darboux Equation and Shifted $k$-Plane Transforms
论文作者
论文摘要
Euler-Poisson-Darboux方程的逆问题涉及从有关其解决方案的不完整信息中重建了该方程的Cauchy数据。在本文中，研究了此问题与移位的$ k $平面变换的注射率有关，该变换分配给$ l^p（\ m athbb {r}^n）$中的函数，它们的平均值在所有k型平面上的平均值均以固定距离的距离为$ k $ planes。考虑了几种概括，包括$ \ mathbb {r}^2 $中固定宽度条的ra变换，以及在$ \ mathbb {r}^3 $中的固定直径管上的类似变换。
The inverse problem for the Euler-Poisson-Darboux equation deals with reconstruction of the Cauchy data for this equation from incomplete information about its solution. In the present article, this problem is studied in connection with the injectivity of the shifted $k$-plane transform, which assigns to functions in $L^p(\mathbb {R}^n)$ their mean values over all k-planes at a fixed distance from the given $k$-planes. Several generalizations, including the Radon transform over strips of fixed width in $\mathbb {R}^2$ and a similar transform over tubes of fixed diameter in $\mathbb {R}^3$, are considered.
