论文标题
关于声纳变换和相关ra transforms的注释
A Note on the Sonar Transform and Related Radon Transforms
论文作者
论文摘要
几何层析成像图中的声纳变换在欧几里得半空间上的功能与以边界超平面为中心的半球上的这些功能的积分。 我们在最小化功能假设下获得了此转换的尖锐$ l^p $ - $ l^q $估计，并获得新的显式反转公式。 主要结果来自声纳变换之间的有趣联系，对抛物线的ra trans子和横向ra transform transpts transform tontrys transform tontrys transform transpers transform tontrys tontrys tontrys tontrys transform tontrys tontrys transpers transps transps transpers transce rabe轴上的横向轴线，符合最后一个坐标轴。
The sonar transform in geometric tomography maps functions on the Euclidean half-space to integrals of those functions over hemispheres centered on the boundary hyperplane. We obtain sharp $L^p$-$L^q$ estimates for this transform and new explicit inversion formulas under minimal assumptions for functions. The main results follow from intriguing connection between the sonar transform, the Radon transform over paraboloids, and the transversal Radon transform, which integrates functions over hyperplanes, meeting the last coordinate axis.
