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

2013/06/24 by R. K. Srivastava, Srivastava, R. K.
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1306.5658

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

arxiv created 2014/06/12 · arxiv updated 2014/06/13

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 Cⁿ as long as it does not completely lay on the level surface of any bi-graded homogeneous harmonic polynomial on \mathbb Cⁿ. Further, we produce examples of such level surfaces.

Citations

• Coxeter system of planes are sets of injectivity for the twisted spherical means on \mathbb Cⁿ

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