Non-harmonic cones are sets of injectivity for the twisted spherical means on ℂⁿ

Srivastava, R.

doi:10.1090/tran/6488

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

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

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