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SUMMARY:Steve Zelditch (Northwestern University)
DTSTART:20220127T170000Z
DTEND:20220127T180000Z
DTSTAMP:20260423T035632Z
UID:Inverse/71
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Inverse/71/"
 >Spatial and Fourier restriction problems for eigenfunctions</a>\nby Steve
  Zelditch (Northwestern University) as part of International Zoom Inverse 
 Problems Seminar\, UC Irvine\n\n\nAbstract\nThere are two different types 
 of “restriction theorems” for Laplace (or related) operators. One type
  is “Fourier restriction theorems” where the Fourier transform is rest
 ricted to a hypersurface or submanifold. Another type is spatial restricti
 on theorems\, where an eigenfunction $\\phi$ of the Laplacian $\\Delta_M$ 
 of a Riemannian manifold is restricted to a submanifold $H$. My talk is ab
 out joint restriction theorems: one first restricts an eigenfunction $\\ph
 i$ to a submanifold $H$\, expands it in eigenfunctions  $e_k$ of $\\Delta_
 H$\, and then studies the Fourier restriction of $\\phi |_H$ to short wind
 ow of Fourier coefficients w.r.t. $H$.  How much of the $L^2$-mass of $\\p
 hi |_H$ lies in a short window of frequencies of $H$?  This kind of proble
 m arises in several branches of analysis. My talk is in part a survey of j
 oint restriction phenomena and in part a description of recent results\, p
 artly in collaboration with Yakun Xi and Emmett Wyman.\n
LOCATION:https://researchseminars.org/talk/Inverse/71/
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