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arXiv · 1506.07425

Heisenberg uniqueness pairs for some algebraic curves in the plane

Deb Kumar Giri·R. K. Srivastava
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Abstract

A Heisenberg uniqueness pair is a pair $\left(Γ, Λ\right)$, where $Γ$ is a curve and $Λ$ is a set in $\mathbb R^2$ such that whenever a finite Borel measure $μ$ having support on $Γ$ which is absolutely continuous with respect to the arc length on $Γ$ satisfies $\hatμ\vert_Λ=0,$ then it is identically $0.$ In this article, we investigate the Heisenberg uniqueness pairs corresponding to the spiral, hyperbola, circle and certain exponential curves. Further, we work out a characterization of the Heisenberg uniqueness pairs corresponding to four parallel lines. In the latter case, we observe a phenomenon of interlacing of three trigonometric polynomials.

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BibTeXRIS

Deb Kumar Giri, R. K. Srivastava. 2017-02-09. Heisenberg uniqueness pairs for some algebraic curves in the plane. https://arxiv.org/abs/1506.07425

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