Restriction of toral eigenfunctions to hypersurfaces and nodal sets

Jean Bourgain; Zeév Rudnick

doi:10.1007/s00039-012-0186-3

Restriction of toral eigenfunctions to hypersurfaces and nodal sets

Jean Bourgain, Zeév Rudnick

School of Mathematical Sciences

Tel Aviv University

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

Abstract

We give uniform upper and lower bounds for the L ² norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. We also present several related results concerning the nodal sets of eigenfunctions.

Original language	English
Pages (from-to)	878-937
Number of pages	60
Journal	Geometric and Functional Analysis
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s00039-012-0186-3
State	Published - Aug 2012

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1007/s00039-012-0186-3

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title = "Restriction of toral eigenfunctions to hypersurfaces and nodal sets",

abstract = "We give uniform upper and lower bounds for the L 2 norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. We also present several related results concerning the nodal sets of eigenfunctions.",

author = "Jean Bourgain and Ze{\'e}v Rudnick",

note = "Funding Information: The authors are indebted to P. Sarnak for many stimulating discussions on the material presented in the paper. J.B. was supported in part by N.S.F. grant DMS 0808042. Z.R. was supported by the Oswald Veblen Fund during his stay at the Institute for Advanced Study and by the Israel Science Foundation (grant No. 1083/10).",

year = "2012",

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AU - Rudnick, Zeév

N1 - Funding Information: The authors are indebted to P. Sarnak for many stimulating discussions on the material presented in the paper. J.B. was supported in part by N.S.F. grant DMS 0808042. Z.R. was supported by the Oswald Veblen Fund during his stay at the Institute for Advanced Study and by the Israel Science Foundation (grant No. 1083/10).

PY - 2012/8

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N2 - We give uniform upper and lower bounds for the L 2 norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. We also present several related results concerning the nodal sets of eigenfunctions.

AB - We give uniform upper and lower bounds for the L 2 norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. We also present several related results concerning the nodal sets of eigenfunctions.

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DO - 10.1007/s00039-012-0186-3

M3 - مقالة

SN - 1016-443X

VL - 22

SP - 878

EP - 937

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 4

ER -

Restriction of toral eigenfunctions to hypersurfaces and nodal sets

Abstract

All Science Journal Classification (ASJC) codes

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