Geodesic restrictions for the Casimir operator

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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 languageEnglish
Pages (from-to)2437-2460
Number of pages24
JournalJournal of Functional Analysis
Volume261
Issue number9
DOIs
StatePublished - 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.

Keywords

  • Hyperbolic operators
  • Representation theory
  • Restriction norm

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