Geodesic restrictions for the Casimir operator

Andre Reznikov

doi:10.1016/j.jfa.2011.06.010

Geodesic restrictions for the Casimir operator

Andre Reznikov

Department of Mathematics

Bar-Ilan University

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

Abstract

We consider the hyperbolic Casimir operator C defined on the tangent sphere bundle SY of a compact hyperbolic Riemann surface Y. We prove a non-trivial bound on the L2-norm of the restriction of eigenfunctions of C to certain natural hypersurfaces in SY. The result that we obtain goes beyond known (sharp) local bounds of L. Hörmander.

Original language	English
Pages (from-to)	2437-2460
Number of pages	24
Journal	Journal of Functional Analysis
Volume	261
Issue number	9
DOIs	https://doi.org/10.1016/j.jfa.2011.06.010
State	Published - 1 Nov 2011

Keywords

Hyperbolic operators
Representation theory
Restriction norm

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/j.jfa.2011.06.010

Cite this

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title = "Geodesic restrictions for the Casimir operator",

abstract = "We consider the hyperbolic Casimir operator C defined on the tangent sphere bundle SY of a compact hyperbolic Riemann surface Y. We prove a non-trivial bound on the L2-norm of the restriction of eigenfunctions of C to certain natural hypersurfaces in SY. The result that we obtain goes beyond known (sharp) local bounds of L. H{\"o}rmander.",

keywords = "Hyperbolic operators, Representation theory, Restriction norm",

author = "Andre Reznikov",

note = "Funding Information: 1 Partially supported by the Veblen Fund at IAS, by a BSF grant, by the ISF Center of Excellency grant 1691/10, and by the Minerva Center at ENI.",

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N1 - Funding Information: 1 Partially supported by the Veblen Fund at IAS, by a BSF grant, by the ISF Center of Excellency grant 1691/10, and by the Minerva Center at ENI.

PY - 2011/11/1

Y1 - 2011/11/1

N2 - We consider the hyperbolic Casimir operator C defined on the tangent sphere bundle SY of a compact hyperbolic Riemann surface Y. We prove a non-trivial bound on the L2-norm of the restriction of eigenfunctions of C to certain natural hypersurfaces in SY. The result that we obtain goes beyond known (sharp) local bounds of L. Hörmander.

AB - We consider the hyperbolic Casimir operator C defined on the tangent sphere bundle SY of a compact hyperbolic Riemann surface Y. We prove a non-trivial bound on the L2-norm of the restriction of eigenfunctions of C to certain natural hypersurfaces in SY. The result that we obtain goes beyond known (sharp) local bounds of L. Hörmander.

KW - Hyperbolic operators

KW - Representation theory

KW - Restriction norm

UR - http://www.scopus.com/inward/record.url?scp=80052101789&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2011.06.010

DO - 10.1016/j.jfa.2011.06.010

M3 - مقالة

SN - 0022-1236

VL - 261

SP - 2437

EP - 2460

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 9

ER -

Geodesic restrictions for the Casimir operator

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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