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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fredholmness vs. Spectral Discreteness for first-order differential operators
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by N. Anghel PDF
Proc. Amer. Math. Soc. 144 (2016), 693-701 Request permission


It is shown that for essentially self-adjoint first-order differential operators $D$, acting on sections of bundles over complete (non-compact) manifolds, Fredholmness vs.$\!$ Spectral Discreteness is the same as ‘$\exists c>0$, $D$ is $c$-invertible at infinity’ vs. ‘$\forall c>0$, $D$ is $c$-invertible at infinity’. An application involving the spectral theory of electromagnetic Dirac operators is then given.
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Additional Information
  • N. Anghel
  • Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
  • MR Author ID: 26280
  • Email:
  • Received by editor(s): November 19, 2014
  • Received by editor(s) in revised form: January 22, 2015
  • Published electronically: June 26, 2015
  • Communicated by: Varghese Mathai
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 693-701
  • MSC (2010): Primary 35P05, 58J50; Secondary 81Q10, 81V10
  • DOI:
  • MathSciNet review: 3430845