Fixed frequency eigenfunction immersions and supremum norms of random waves

Yaiza Canzani; Boris Hanin

doi:10.3934/era.2015.22.76

Fixed frequency eigenfunction immersions and supremum norms of random waves

Yaiza Canzani, Boris Hanin

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of Burq-Lebeau and others on upper bounds for the sup-norms of random linear combinations of high frequency eigenfunctions.

Original language	English (US)
Pages (from-to)	76-86
Number of pages	11
Journal	Electronic Research Announcements in Mathematical Sciences
Volume	22
DOIs	https://doi.org/10.3934/era.2015.22.76
State	Published - Aug 31 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Immersions by eigenfunctions
Random waves
Supremum norms

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10.3934/era.2015.22.76

Cite this

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abstract = "A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of Burq-Lebeau and others on upper bounds for the sup-norms of random linear combinations of high frequency eigenfunctions.",

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AU - Hanin, Boris

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AB - A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of Burq-Lebeau and others on upper bounds for the sup-norms of random linear combinations of high frequency eigenfunctions.

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KW - Random waves

KW - Supremum norms

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JO - Electronic Research Announcements in Mathematical Sciences

JF - Electronic Research Announcements in Mathematical Sciences

ER -

Fixed frequency eigenfunction immersions and supremum norms of random waves

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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