Quantum ergodic restriction for cauchy data: Interior que and restricted que

Hans Christianson, John A. Toth, Steve Zelditch

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We prove a quantum ergodic restriction theorem for the Cauchy data of a sequence of quantum ergodic eigenfunctions on a hypersurface H of a Riemannian manifold (M, g). The technique of proof is to use a Rellich-type identity to relate quantum ergodicity of Cauchy data on H to quantum ergodicity of eigenfunctions on the global manifold M. This has the interesting consequence that if the eigenfunctions are quantum uniquely ergodic on the global manifold M, then the Cauchy data is automatically quantum uniquely ergodic on H with respect to operators whose symbols vanish to order one on the glancing set of unit tangential directions to H.

Original languageEnglish (US)
Pages (from-to)465-475
Number of pages11
JournalMathematical Research Letters
Issue number3
StatePublished - May 2013

ASJC Scopus subject areas

  • Mathematics(all)


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