Coxeter线系是$\mathbb C$上扭球平均的内射集
Coxeter system of lines are sets of injectivity for the twisted spherical means on $\mathbb C$
摘要：
众所周知，$\mathbb R^2$中的直线不是关于该直线的奇函数的球面平均的内射性的集合。证明了对于每个谱投影$ e^{\frac{1}{4}|z|^2}f\timesφ_k$为多项式的函数$f\in L^2(\mathbb C),$，通过原点的任意直线都是扭球平均（TSM）的内射集。然后，我们证明了任何偶数行的Coxeter系统都是$L^q(\mathbb C),~1\leq q\leq2.$的TSM的内射集
英文摘要：
It is well known that a line in $\mathbb R^2$ is not a set of injectivity for the spherical means for odd functions about that line. We prove that any line passing through the origin is a set of injectivity for the twisted spherical means (TSM) for functions $f\in L^2(\mathbb C),$ whose each of spectral projection $ e^{\frac{1}{4}|z|^2}f\timesφ_k$ is a polynomial. Then, we prove that any Coxeter system of even number of lines is a set of injectivity for the TSM for $L^q(\mathbb C),~1\leq q\leq2.$
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