局部紧群上卷积算子的谱分析
Spectral analysis for convolution operators on locally compact groups
摘要：
我们考虑局部紧群上具有测度$μ$的卷积算子$H_μ$.通过构造核分别包含$H_μ$的纯点子空间和奇异子空间的辅助算子，刻画了$H_μ$的谱.证明依赖于换位子方法。
英文摘要：
We consider operators $H_μ$ of convolution with measures $μ$ on locally compact groups. We characterize the spectrum of $H_μ$ by constructing auxiliary operators whose kernel contain the pure point and singular subspaces of $H_μ$, respectively. The proofs rely on commutator methods.
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