Coxeter system of lines are sets of injectivity for the twisted spherical means on $\mathbb C$

Details Coxeter system of lines are sets of injectivity for the twisted spherical means on $\mathbb C$ Coxeter system of lines are sets of injectivity for the twisted spherical means on $\mathbb C$

2011-03-23

arxiv.org/abs/1103.4571v9

Mathematics

Functional Analysis

I have updated the manuscript and added one more remark about Heisenberg uniqueness pairs (HUP) at the end

Scientific paper

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^1/4|z|^2}f\times\varphi_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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