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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Semiclassical Cauchy estimates and applications
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by Long Jin PDF
Trans. Amer. Math. Soc. 369 (2017), 975-995 Request permission

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