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Quantum ergodic restriction for Cauchy data: Interior QUE and restricted QUE
Quantum ergodic restriction Cauchy data Interior QUE restricted QUE Analysis of PDEs
2012/5/24
We prove a quantum ergodic restriction theorem for the Cauchy data of a sequence of quantum ergodic eigenfunctions on a hypersurface $H$ of a Riemannian manifold $(M, g)$. The technique of proof is to...
Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities For Paraboloids
Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities Paraboloids
2011/1/19
Let Pd−1 be the paraboloid in Rd,Pd−1 = {(y′, yd) ∈ Rd−1 × R : yd = |y′|2/2}.Equip Pd−1 with the appropriately dilation-invariant measure on Rd defined by Z Rd f(y′, yd) d(y...