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Lp norm estimates of eigenfunctions restricted to submanifolds
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Rui Hu
Published/Copyright:
September 3, 2009
Abstract
We study the growth rate of Lp norms of eigenfunctions of the Laplace-Beltrami operator restricted to submanifolds of compact C∞ Riemannian manifolds. The spectral projection operators can be expressed as oscillatory integral operators, so the question reduces to oscillatory integral operator norm estimates. We study the relationship between the extrinsic geometry of these submanifolds and the canonical relations associated to these oscillatory integral operators.
Received: 2007-06-04
Revised: 2008-04-08
Published Online: 2009-09-03
Published in Print: 2009-November
© de Gruyter 2009
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Articles in the same Issue
- A Hopf theorem for open surfaces in product spaces
- On R. Steinberg's theorem on algebras of coinvariants
- Natural pseudo-distances between closed curves
- Clifford semigroups of ideals in monoids and domains
- Lp norm estimates of eigenfunctions restricted to submanifolds
- Central values of generalized multiple sine functions
- Lp-independence of spectral bounds of non-local Feynman-Kac semigroups
- On pairwise mutually permutable products
- The block structure spaces of real projective spaces and orthogonal calculus of functors II
- Erratum to: “Intrinsic ultracontractivity for non-symmetric Lévy processes” [Forum Math. 21 (2009) 43–66]
