• Media type: E-Article
  • Title: ON INTEGRALS OF EIGENFUNCTIONS OVER GEODESICS
  • Contributor: CHEN, XUEHUA; SOGGE, CHRISTOPHER D.
  • imprint: American Mathematical Society, 2015
  • Published in: Proceedings of the American Mathematical Society
  • Language: English
  • ISSN: 0002-9939; 1088-6826
  • Origination:
  • Footnote:
  • Description: <p>If (M, g) is a compact Riemannian surface, then the integrals of L2-(M)-normalized eigenfunctions ej over geodesic segments of fixed length are uniformly bounded. Also, if (M, g) has negative curvature and γ(t) is a geodesic parameterized by arc length, the measures ej(γ(t)) dt on ℝ tend to zero in the sense of distributions as the eigenvalue λj → ∞, and so integrals of eigenfunctions over periodic geodesics tend to zero as λj → ∞. The assumption of negative curvature is necessary for the latter result.</p>
  • Access State: Open Access