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Upper Bounds on the Size of Nodal Sets for Gevrey and Quasianalytic Riemannian Manifolds

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Abstract

We find new polynomial upper bounds for the size of nodal sets of eigenfunctions when the Riemannian manifold has a Gevrey or quasianalytic regularity.

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Notes

  1. A result of this type was first proved by Hörmander for operators with analytic coefficients.

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Acknowledgements

The author is thankful to Steve Zelditch for his comments on the first draft of this article and for bringing to attention the works of [Hi50] and [NaSoVo04]. The author is grateful to the referees for their very helpful comments and for pointing out numerous errors. The research of the author is supported by the Simons Collaborations Grants for Mathematicians 638398.

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  1. Department of Mathematics, UC Irvine, Irvine, CA, 92697, USA

    Hamid Hezari

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  1. Hamid Hezari
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Hezari, H. Upper Bounds on the Size of Nodal Sets for Gevrey and Quasianalytic Riemannian Manifolds. Commun. Math. Phys. 404, 1341–1359 (2023). https://doi.org/10.1007/s00220-023-04853-z

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