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Perron-Frobenius operators and the Klein-Gordon equation

Francisco Canto-Martín; Håkan Hedenmalm; Alfonso Montes-Rodríguez — 2014

Journal of the European Mathematical Society

For a smooth curve $Γ$ and a set $Λ$ in the plane $ℝ^{2}$ , let $A C (Γ; Λ)$ be the space of finite Borel measures in the plane supported on $Γ$ , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on $Λ$ . Following [12], we say that $(Γ, Λ)$ is a Heisenberg uniqueness pair if $A C (Γ; Λ) = {0}$ . In the context of a hyperbola $Γ$ , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets $Λ$ of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the...

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