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

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

3 Scopus citations

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

Bibliographical 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.

Funding

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.

Funders	Funder number
ISF Center of Excellency	1691/10
Veblen Fund
Institute of Advanced Studies, University of Bristol
United States-Israel Binational Science Foundation
Minerva Center for Movement Ecology, Hebrew University of Jerusalem

Keywords

Hyperbolic operators
Representation theory
Restriction norm

Access to Document

10.1016/j.jfa.2011.06.010

Cite this

@article{f255b677e24742cfa61e42c9dee80f37,

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.",

year = "2011",

month = nov,

day = "1",

doi = "10.1016/j.jfa.2011.06.010",

language = "אנגלית",

volume = "261",

pages = "2437--2460",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "9",

}

TY - JOUR

T1 - Geodesic restrictions for the Casimir operator

AU - Reznikov, Andre

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 - https://www.scopus.com/pages/publications/80052101789

U2 - 10.1016/j.jfa.2011.06.010

DO - 10.1016/j.jfa.2011.06.010

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:80052101789

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

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this