散射理论和SL（2，R）径向部分的指数定理
Scattering theory and an index theorem on the radial part of SL(2,R)
摘要：
给出了Casimir算子作用在SL（2，R）径向部分上的谱理论和散射理论.经过适当的分解，这些调查包括在研究一个家庭的微分算子作用在半线。对于这些算子，可以用高斯超几何函数找到预解式、谱密度和Moeller波算子的显式表达式。一个指标定理也介绍和讨论。由此产生的等式将超几何函数的各种渐进行为联系起来。
英文摘要：
We present the spectral and scattering theory of the Casimir operator acting on the radial part of SL(2,R). After a suitable decomposition, these investigations consist in studying a family of differential operators acting on the half-line. For these operators, explicit expressions can be found for the resolvent, for the spectral density, and for the Moeller wave operators, in terms of the Gauss hypergeometric function. An index theorem is also introduced and discussed. The resulting equality links various asymptotic behaviors of the hypergeometric function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
