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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Weighted CLR type bounds in two dimensions
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by Rupert L. Frank, Ari Laptev and Larry Read
Trans. Amer. Math. Soc. 377 (2024), 3357-3371
DOI: https://doi.org/10.1090/tran/9124
Published electronically: February 26, 2024

Abstract:

We derive weighted versions of the Cwikel–Lieb–Rozenblum inequality for the Schrödinger operator in two dimensions with a nontrivial Aharonov–Bohm magnetic field. Our bounds capture the optimal dependence on the flux and we identify a class of long-range potentials that saturate our bounds in the strong coupling limit. We also extend our analysis to the two-dimensional Schrödinger operator acting on antisymmetric functions and obtain similar results.
References
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Bibliographic Information
  • Rupert L. Frank
  • Affiliation: Mathematisches Institut, Ludwig-Maximilans Universität München, Theresienstr. 39, 80333 München, Germany, Munich Center for Quantum Science and Technology, Schellingstr. 4, 80799 München, Germany, and Mathematics 253-37, Caltech, Pasadena, California 91125
  • MR Author ID: 728268
  • ORCID: 0000-0001-7973-4688
  • Email: r.frank@lmu.de
  • Ari Laptev
  • Affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom, and Sirius Mathematics Center, Sirius University of Science and Technology, 1 Olympic Ave, 354340, Sochi, Russia
  • MR Author ID: 292869
  • Email: a.laptev@imperial.ac.uk
  • Larry Read
  • Affiliation: Mathematisches Institut, Ludwig-Maximilans Universität München, Theresienstr. 39, 80333 München, Germany
  • MR Author ID: 1520686
  • ORCID: 0000-0003-2744-5854
  • Email: read@math.lmu.de
  • Received by editor(s): March 15, 2023
  • Received by editor(s) in revised form: October 23, 2023
  • Published electronically: February 26, 2024
  • Additional Notes: The first author was partially supported through US National Science Foundation grant DMS-1954995, as well as through the Excellence Strategy of the German Research Foundation grant EXC-2111-390814868 and through German Research Foundation project TRR 352 - Project-ID 470903074. The second author was supported by the Ministry of Science and Higher Education of the Russian Federation (Agreement 075-10-2021-093, Project MTH-RND-2124).The third author was partially supported through German Research Foundation project TRR 352 - Project-ID 470903074.
  • © Copyright 2024 by the authors
  • Journal: Trans. Amer. Math. Soc. 377 (2024), 3357-3371
  • MSC (2020): Primary 35P15; Secondary 81Q10
  • DOI: https://doi.org/10.1090/tran/9124