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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nodal sets for sums of eigenfunctions on Riemannian manifolds


Author: Harold Donnelly
Journal: Proc. Amer. Math. Soc. 121 (1994), 967-973
MSC: Primary 58G25
MathSciNet review: 1205487
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Abstract: Quantitative versions of unique continuation are proved for finite sums of eigenfunctions of the Laplacian on compact Riemannian manifolds. The results include a lower bound for the order of vanishing, a growth estimate for the supremum on compact balls, and a gradient bound. For real analytic metrics, an upper bound for the Hausdorff measure of the zero set is derived.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1205487-X
PII: S 0002-9939(1994)1205487-X
Article copyright: © Copyright 1994 American Mathematical Society