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Proceedings of the American Mathematical Society

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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.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1994-1205487-X
Article copyright: © Copyright 1994 American Mathematical Society