Bounds for spectral projectors on tori

Pierre Germain, Simon L. Rydin Myerson

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate norms of spectral projectors on thin spherical shells for the Laplacian on tori. This is closely related to the boundedness of resolvents of the Laplacian and the boundedness of norms of eigenfunctions of the Laplacian. We formulate a conjecture and partially prove it.

Original languageEnglish (US)
Article numbere24
JournalForum of Mathematics, Sigma
Volume10
DOIs
StatePublished - May 12 2022

Keywords

  • discrete restriction
  • geometry of numbers
  • l2 decoupling
  • lattice points in convex bodies
  • Lp resolvent estimates
  • Spectral projectors

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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