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arXiv · 1507.02624

Non-harmonic cones are Heisenberg uniqueness pairs for the Fourier transform on $\mathbb R^n$

R. K. Srivastava
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Abstract

In this article, we prove that a cone is a Heisenberg uniqueness pair corresponding to sphere as long as the cone does not completely recline on the level surface of any homogeneous harmonic polynomial on $\mathbb R^n.$ We derive that $\left(S^2, \text{ paraboloid}\right)$ and $\left(S^2, \text{ geodesic of } S_r(o)\right)$ are Heisenberg uniqueness pairs for a class of certain symmetric finite Borel measures in $\mathbb R^3.$ Further, we correlate the problem of Heisenberg uniqueness pairs to the sets of injectivity for the spherical mean operator.

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BibTeXRIS

R. K. Srivastava. 2015-07-08. Non-harmonic cones are Heisenberg uniqueness pairs for the Fourier transform on $\mathbb R^n$. https://arxiv.org/abs/1507.02624

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