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Semiclassical $L^p$ quasimode restriction estimates in two dimensions

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arxiv 2401.16881 v3 pith:DYW7QEHG submitted 2024-01-30 math.AP math.CAmath.SP

classification math.APmath.CAmath.SP
keywords estimatesrestrictioncurvedimensionssemiclassicalsmoothaddressanalysis
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abstract

We establish the $L^p$ restriction estimates for quasimodes on a smooth curve in two dimensions. Our estimates are sharp for all smooth curves. As an application, we address $L^p$ eigenfunction restriction estimates for Laplace-Beltrami eigenfunctions on $2$-dimensional compact Riemannian manifolds without boundary and Hermite functions on $\mathbb R^2$. Our method involves a geometric analysis of the contact order between the curve and the bicharacteristic flow of the semiclassical pseudodifferential operator.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Endpoint Eigenfunction Bound for the Hermite Operator in Two Dimensions

    math.CA 2026-07 conditional novelty 7.0 of 10

    The missing endpoint L^2→L^{10/3} bound for Hermite spectral projections in two dimensions, with the optimal λ^{-1/10} decay, is proved.

  2. Sharp estimates for the Fourier transform of surface-carried measures and maximal operators associated with hypersurfaces in $\mathbb{R}^4$ with vanishing Gaussian curvature

    math.CA 2026-02 conditional novelty 6.0 of 10

    For polynomial graphs in R^4 with identically zero Hessian determinant, oscillatory integral decay and maximal-operator boundedness exponents are determined by the Newton-polyhedron height h(φ).

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