On a spectral theorem of Weyl
On a spectral theorem of Weyl
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关于韦尔谱定理
DOI：
10.1016/j.exmath.2020.02.001
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发表时间：
2016
影响因子：
0.7
通讯作者：
Qijun Tan
中科院分区：
文献类型：
--
作者：
N. Higson;Qijun Tan
给出了渐近常系数半直线上Sturm-Liouville算子谱的连续部分的Weyl定理的一个新证明。早期的论点，由于Weyl和Kodaira，依赖于线性常微分算子的格林函数的特殊性质。我们使用了具有几何起源的C∗-代数表示的渐近包含的概念。我们将这一概念应用于约化群上球函数的Plancherel公式。
We give a new proof of a theorem of Weyl on the continuous part of the spectrum of Sturm–Liouville operators on the half-line with asymptotically constant coefficients. Earlier arguments, due to Weyl and Kodaira, depended on particular features of Green’s functions for linear ordinary differential operators. We use a concept of asymptotic containment of C∗-algebra representations that has geometric origins. We apply the concept elsewhere to the Plancherel formula for spherical functions on reductive groups.