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Lower bounds on eigenfunctions on hyperbolic surfaces. Dyatlov, Semyon
Description
I show that on a compact hyperbolic surface, the mass of an L2- normalized eigenfunction of the Laplacian on any nonempty open set is bounded below by a positive constant depending on the set, but not on the eigenvalue. This statement, more precisely its stronger semiclassi- cal version, has many applications including control for the Schrdinger equation and the full support property for semiclassical defect mea- sures. The key new ingredient of the proof is a fractal uncertainty principle, stating that no function can be localized close to a porous set in both position and frequency. This talk is based on joint works with Long Jin and with Jean Bourgain.
Item Metadata
Title |
Lower bounds on eigenfunctions on hyperbolic surfaces.
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-03-21T19:33
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Description |
I show that on a compact hyperbolic surface, the mass of an L2-
normalized eigenfunction of the Laplacian on any nonempty open set is
bounded below by a positive constant depending on the set, but not on
the eigenvalue. This statement, more precisely its stronger semiclassi-
cal version, has many applications including control for the Schrdinger
equation and the full support property for semiclassical defect mea-
sures. The key new ingredient of the proof is a fractal uncertainty
principle, stating that no function can be localized close to a porous
set in both position and frequency. This talk is based on joint works
with Long Jin and with Jean Bourgain.
|
Extent |
48 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Massachusetts Institute of Technology
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Series | |
Date Available |
2018-09-18
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0372065
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International