Non-harmonic cones are sets of injectivity for the twisted spherical means on $\mathbb C^n$

摘要

In this article, we prove that a complex cone is a set of injectivity for thetwisted spherical means for the class of all continuous functions on $\mathbbC^n$ as long as it does not completely lay on the level surface of anybi-graded homogeneous harmonic polynomial on $\mathbb C^n.$ Further, we produceexamples of such level surfaces.