论文标题
SL（2，R）的径向部分的散射理论和索引定理
Scattering theory and an index theorem on the radial part of SL(2,R)
论文作者
论文摘要
我们介绍了作用于SL（2，R）径向部分的Casimir操作员的光谱和散射理论。经过合适的分解后，这些研究包括研究一个在半线上作用的差异操作员家族。对于这些操作员，就高斯超几何函数而言，可以为分解，光谱密度和Moeller波算子找到明确的表达式。还介绍和讨论了索引定理。产生的平等链接了超几何函数的各种渐近行为。
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.
