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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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Eigenvalue asymptotics and exponential decay of eigenfunctions for Schrödinger operators with magnetic fields
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by Zhongwei Shen
Trans. Amer. Math. Soc. 348 (1996), 4465-4488
DOI: https://doi.org/10.1090/S0002-9947-96-01709-6

Abstract:

We consider the Schrödinger operator with magnetic field, \begin{equation*}H=(\frac {1}{i}\nabla -{\overset {\rightharpoonup }{a}}(x))^{2}+V(x) \text { in } \mathbb {R}^{n}. \end{equation*} Assuming that $V\ge 0$ and $|\text {curl} \overset {\rightharpoonup }{a}|+V+1$ is locally in certain reverse Hölder class, we study the eigenvalue asymptotics and exponential decay of eigenfunctions.
References
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Bibliographic Information
  • Zhongwei Shen
  • Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
  • MR Author ID: 227185
  • Email: shenz@ms.uky.edu
  • Received by editor(s): May 19, 1995
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 4465-4488
  • MSC (1991): Primary 35P20, 35J10
  • DOI: https://doi.org/10.1090/S0002-9947-96-01709-6
  • MathSciNet review: 1370650