论文标题
ra transform：双对和不可约的表示
Radon Transform: Dual Pairs and Irreducible Representations
论文作者
论文摘要
我们说明了[Siam J. Math。肛门，51（6），4356-4381]，可以被描述为Helgason的双$ G $ hoshosiens对$（x，ξ）$的变体，这使我们能够证明许多现有radon变换的属性和倒置属性和反转公式。在这里，我们详细分析了双对理论中的重要方面之一，即地图标签至manifold $ξ\ to \ hatT配给\ hatT配给\ hatT配给$，我们证明这是$ g $在$ l^2（2（ξ）$上的$ g $的不可约会的必要条件。我们进一步解释了[Siam J. Math。肛门，51（6），4356-4381]适用于$ \ Mathbb r^3 $中的经典ra和X射线变换。
We illustrate the general point of view developed in [SIAM J. Math. Anal., 51(6), 4356-4381] that can be described as a variation of Helgason's theory of dual $G$-homogeneous pairs $(X,Ξ)$ and which allows us to prove intertwining properties and inversion formulae of many existing Radon transforms. Here we analyze in detail one of the important aspects in the theory of dual pairs, namely the injectivity of the map label-to-manifold $ξ\to\hatξ$ and we prove that it is a necessary condition for the irreducibility of the quasi-regular representation of $G$ on $L^2(Ξ)$. We further explain how the theory in [SIAM J. Math. Anal., 51(6), 4356-4381] applies to the classical Radon and X-ray transforms in $\mathbb R^3$.
