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Semiclassical Cauchy estimates and applications


Author: Long Jin
Journal: Trans. Amer. Math. Soc. 369 (2017), 975-995
MSC (2010): Primary 35J10; Secondary 32D15, 58J50
DOI: https://doi.org/10.1090/tran/6715
Published electronically: March 18, 2016
MathSciNet review: 3572261
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Abstract: 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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Additional Information

Long Jin
Affiliation: Department of Mathematics, Evans Hall, University of California, Berkeley, California 94720
Email: jinlong@math.berkeley.edu

DOI: https://doi.org/10.1090/tran/6715
Received by editor(s): March 26, 2013
Received by editor(s) in revised form: February 2, 2015
Published electronically: March 18, 2016
Article copyright: © Copyright 2016 American Mathematical Society