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

R. K. Srivastava

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

Functional Analysis 2014-06-13 v7

Authors: R. K. Srivastava

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.

Keywords

non-harmonic cones sets of injectivity twisted spherical means complex cone bi-graded homogeneous harmonic polynomials $\mathbb c^n$

Cite

@article{arxiv.1306.5658,
  title  = {Non-harmonic cones are sets of injectivity for the twisted spherical means on $\mathbb C^n$},
  author = {R. K. Srivastava},
  journal= {arXiv preprint arXiv:1306.5658},
  year   = {2014}
}

Comments

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

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

Abstract

Keywords

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