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Fredholmness vs. Spectral Discreteness for first-order differential operators


Author: N. Anghel
Journal: Proc. Amer. Math. Soc. 144 (2016), 693-701
MSC (2010): Primary 35P05, 58J50; Secondary 81Q10, 81V10
DOI: https://doi.org/10.1090/proc12741
Published electronically: June 26, 2015
MathSciNet review: 3430845
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Abstract: 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
Email: anghel@unt.edu

DOI: https://doi.org/10.1090/proc12741
Keywords: First-order differential operator, Fredholm operator, discrete spectrum, propagation speed, electromagnetic Dirac operator
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
Article copyright: © Copyright 2015 American Mathematical Society