Heisenberg uniqueness pairs for some algebraic curves in the plane

2015/06/24 by Deb Kumar Giri, Giri, Deb Kumar, R. K. Srivastava +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic and Geometric Analysis #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1506.07425

Abstract

A Heisenberg uniqueness pair is a pair (Γ, Λ), where Γ is a curve and Λ is a set in \mathbb R² 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 μ\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.

Cited by

• Uniqueness of the group Fourier transform on certain nilpotent Lie groups

Related

• Heisenberg uniqueness pairs for some algebraic curves and surfaces
• A dynamical system approach to Heisenberg Uniqueness Pairs
• Heisenberg Uniqueness Pairs and the wave equation
• Heisenberg uniqueness pairs corresponding to finite number of parallel\n lines
• A note on discrete Heisenberg uniqueness pairs for the parabola