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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>