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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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On the trace of Schrödinger heat kernels and regularity of potentials
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by Hart Smith PDF
Trans. Amer. Math. Soc. 371 (2019), 3857-3875 Request permission

Abstract:

For the Schrödinger operator $-\Delta _{\mathrm {g}}+V$ on a complete Riemannian manifold with real valued potential $V$ of compact support, we establish a sharp equivalence between Sobolev regularity of $V$ and the existence of finite-order asymptotic expansions as $t\rightarrow 0$ of the relative trace of the Schrödinger heat kernel. As an application, we generalize a result of Sà Barreto and Zworski concerning the existence of resonances on compact metric perturbations of Euclidean space to the case of bounded measurable potentials.
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Additional Information
  • Hart Smith
  • Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
  • MR Author ID: 264225
  • Email: hfsmith@uw.edu
  • Received by editor(s): March 21, 2017
  • Received by editor(s) in revised form: September 13, 2017
  • Published electronically: December 3, 2018
  • Additional Notes: This material is based upon work supported by the National Science Foundation under Grant DMS-1500098
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 3857-3875
  • MSC (2010): Primary 58J35; Secondary 35P25
  • DOI: https://doi.org/10.1090/tran/7486
  • MathSciNet review: 3917211