Semiclassical Cauchy estimates and applications

In this note, we consider the solutions to semiclassical analytic Schrödinger equations and prove a semiclassical version of the Cauchy estimate. As an application, we study the asymptotics for the Hausdorff measures of the nodal sets of the solutions on a compact analytic manifold as h\to 0.

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2017-02, Vol.369 (2), p.975-995
Main Author: JIN, LONG
Format: Article
Language:English
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Summary:In this note, we consider the solutions to semiclassical analytic Schrödinger equations and prove a semiclassical version of the Cauchy estimate. As an application, we study the asymptotics for the Hausdorff measures of the nodal sets of the solutions on a compact analytic manifold as h\to 0.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6715