Geodesic
Perron-Frobenius operators and the Klein-Gordon equation
Journal of the European Mathematical Society, Tome 16 (2014) no. 1, pp. 31-66 Cet article a éte moissonné depuis la source EMS Press

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For a smooth curve Γ and a set Λ in the plane R2, let AC(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 AC(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 issue of finding the dimension of AC(Γ;Λ) when it is non-zero. We will fix the curve Γ to be the hyperbola x1​x2​=1, and the set Λ=Λα,β​ to be the lattice-cross
DOI : 10.4171/jems/427
Classification : 42-XX, 11-XX, 31-XX, 58-XX
Keywords: Trigonometric system, inversion, Perron–Frobenius operator, Koopman operator, invariant measure, Klein–Gordon equation, ergodic theory 
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     title = {Perron-Frobenius operators and the {Klein-Gordon} equation},
     journal = {Journal of the European Mathematical Society},
     pages = {31--66},
     year = {2014},
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     number = {1},
     doi = {10.4171/jems/427},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/427/}
}
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Francisco Canto-Martín; Haakan Hedenmalm; Alfonso Montes-Rodríguez. Perron-Frobenius operators and the Klein-Gordon equation. Journal of the European Mathematical Society, Tome 16 (2014) no. 1, pp. 31-66. doi: 10.4171/jems/427

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