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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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On the structure of spectra of periodic elliptic operators
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by Peter Kuchment and Sergei Levendorskiî PDF
Trans. Amer. Math. Soc. 354 (2002), 537-569 Request permission

Abstract:

The paper discusses the problem of absolute continuity of spectra of periodic elliptic operators. A new result on absolute continuity for a matrix operator of Schrödinger type is obtained. It is shown that all types of operators for which the absolute continuity has previously been established can be reduced to this one. It is also discovered that some natural generalizations stumble upon an obstacle in the form of non-triviality of a certain analytic bundle on the two-dimensional torus.
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Additional Information
  • Peter Kuchment
  • Affiliation: Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033
  • Address at time of publication: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
  • MR Author ID: 227235
  • ORCID: canUsePostMessage
  • Email: kuchment@math.tamu.edu
  • Sergei Levendorskiî
  • Affiliation: Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033
  • Address at time of publication: Department of Mathematics, Rostov State Academy of Economics, Rostov-on-Don, Russia
  • Email: leven@ns.rnd.runnet.ru
  • Received by editor(s): October 3, 2000
  • Published electronically: September 21, 2001
  • Additional Notes: The first author was supported in part by an NRC COBASE Grant, NSF Grants DMS 9610444 and DMS 0072248, and by a DEPSCoR Grant
    The second author was supported in part by an NRC COBASE Grant.
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 537-569
  • MSC (2000): Primary 35P99; Secondary 35J10
  • DOI: https://doi.org/10.1090/S0002-9947-01-02878-1
  • MathSciNet review: 1862558