Equidistribution of toral eigenfunctions along hypersurfaces
نویسندگان
چکیده
منابع مشابه
Restriction of Toral Eigenfunctions to Hypersurfaces
Let T = R/Z be the d-dimensional flat torus. We establish for d = 2, 3 uniform upper and lower bounds on the restrictions of the eigenfunctions of the Laplacian to smooth hyper-surfaces with non-vanishing curvature.
متن کاملRestriction of Toral Eigenfunctions to Hypersurfaces and Nodal Sets
We give uniform upper and lower bounds for the L norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. We also present several related results concerning the nodal sets of eigenfunctions.
متن کاملOn the nodal sets of toral eigenfunctions
We study the nodal sets of eigenfunctions of the Laplacian on the standard d-dimensional flat torus. The question we address is: Can a fixed hypersurface lie on the nodal sets of eigenfunctions with arbitrarily large eigenvalue? In dimension two, we show that this happens only for segments of closed geodesics. In higher dimensions, certain cylindrical sets do lie on nodal sets corresponding to ...
متن کاملSmall Scale Equidistribution of Eigenfunctions on the Torus
We study the small scale distribution of the L2 mass of eigenfunctions of the Laplacian on the flat torus Td . Given an orthonormal basis of eigenfunctions, we show the existence of a density one subsequencewhose L2 mass equidistributes at small scales. In dimension two our result holds all the way down to the Planck scale. For dimensions d = 3, 4 we can restrict to individual eigenspaces and s...
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It is well known that (i) for every irrational number α the Kronecker sequence mα (m = 1, . . . ,M) is equidistributed modulo one in the limit M → ∞, and (ii) closed horocycles of length l become equidistributed in the unit tangent bundle T1M of a hyperbolic surface M of finite area, as l → ∞. In the present paper both equidistribution problems are studied simultaneously: we prove that for any ...
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2019
ISSN: 0213-2230
DOI: 10.4171/rmi/1135