Non-harmonic cones are Heisenberg uniqueness pairs for the Fourier transform on \mathbb Rⁿ

2015/07/08 by R. K. Srivastava, Srivastava, R. K. · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1507.02624

openalex publication_date 2015/07/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 Rⁿ. We derive that (S², paraboloid) and (S², geodesic of S_r(o)) are Heisenberg uniqueness pairs for a class of certain symmetric finite Borel measures in \mathbb R³. Further, we correlate the problem of Heisenberg uniqueness pairs to the sets of injectivity for the spherical mean operator.

Citations

• The Cramer-Wold theorem on quadratic surfaces and Heisenberg uniqueness\n pairs

Cited by

• Fourier nonuniqueness sets for the hyperbola and the Perron-Frobenius operators

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