L 2 -restriction bounds for eigenfunctions along curves in the quantum completely integrable case
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Bibliographic record
Abstract
Abstract. We show that for a quantum completely integrable system in two dimensions,the L2-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds of the form R γ |ϕ � j |2ds = O( | log �|) for generic curves γ on the surface. We also prove that the maximal restriction bounds of Burq-Gerard-Tzvetkov [BGT] are always attained for certain exceptional subsequences of eigenfunctions. 1.
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|---|---|---|
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