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

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.

This article is accepted in Trans. Amer. Math. Soc. arXiv admin note: text overlap with arXiv:1204.2773

References in corpus (3)

• On the injectivity of the circular Radon transform arising in thermoacoustic tomography
• Coxeter system of lines are sets of injectivity for the twisted spherical means on $\mathbb{C}$
• Real analytic expansion of spectral projection and extension of Hecke-Bochner identity