Semiclassical Cauchy estimates and applications
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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 $h\to 0$.References
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Additional Information
- Long Jin
- Affiliation: Department of Mathematics, Evans Hall, University of California, Berkeley, California 94720
- MR Author ID: 1076590
- Email: jinlong@math.berkeley.edu
- Received by editor(s): March 26, 2013
- Received by editor(s) in revised form: February 2, 2015
- Published electronically: March 18, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 975-995
- MSC (2010): Primary 35J10; Secondary 32D15, 58J50
- DOI: https://doi.org/10.1090/tran/6715
- MathSciNet review: 3572261