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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 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Semiclassical Moser–Trudinger inequalities
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by Rakesh Arora, Phan Thành Nam and Phuoc-Tai Nguyen;
Trans. Amer. Math. Soc. 377 (2024), 3243-3260
DOI: https://doi.org/10.1090/tran/9146
Published electronically: March 20, 2024

Abstract:

We extend the Moser–Trudinger inequality of one function to systems of orthogonal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfunctions of Schrödinger operators on bounded domains.
References
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Bibliographic Information
  • Rakesh Arora
  • Affiliation: Department of Mathematical Sciences, Indian Institute of Technology Varanasi (IIT-BHU), Uttar Pradesh-221005, India
  • MR Author ID: 1323295
  • ORCID: 0000-0002-4491-7596
  • Email: rakesh.mat@iitbhu.ac.in, arora.npde@gmail.com
  • Phan Thành Nam
  • Affiliation: Department of Mathematics, LMU Munich, Theresienstrasse 39, D-80333 Munich, and Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 Munich, Germany
  • MR Author ID: 850145
  • ORCID: 0000-0001-7599-9742
  • Email: nam@math.lmu.de
  • Phuoc-Tai Nguyen
  • Affiliation: Department of Mathematics and Statistics, Masaryk University, Brno, Czechia
  • MR Author ID: 938248
  • Email: ptnguyen@math.muni.cz
  • Received by editor(s): July 3, 2023
  • Published electronically: March 20, 2024
  • Additional Notes: This work has been prepared with the support of Czech Science Foundation, Project GA22-17403S for the three authors. The second author was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC-2111-390814868. The first author was partially supoprted by the Start-up Research Grant (SRG) SRG/2023/000308, Science and Engineering Research Board (SERB), India, and Seed grant IIT(BHU)/DMS/2023-24/493.
  • © Copyright 2024 by the authors
  • Journal: Trans. Amer. Math. Soc. 377 (2024), 3243-3260
  • MSC (2020): Primary 26D10, 26D15, 35A23
  • DOI: https://doi.org/10.1090/tran/9146
  • MathSciNet review: 4744779