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Eigenvalue counting estimates for a class of linear spectral pencils with applications to zero modes

Elton, Daniel and Ta, Tri Ngoc (2012) Eigenvalue counting estimates for a class of linear spectral pencils with applications to zero modes. Journal of Mathematical Analysis and Applications, 391 (2). pp. 613-618. ISSN 0022-247X

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Abstract

Consider a linear spectral pencil of the form P(−i∇)− zQ(x), z ∈ C. If P−1 ∈ weak-Lp and Q ∈ Lp for some 1 < p <∞, it is shown that the total number of eigenvalues with |z|<R is bounded by C[||P−1||∗Lpw||Q||Lp R]p. An application is made to estimate the frequency with which zero modes of the Weyl–Dirac operator occur when the magnetic potential is scaled.

Item Type: Article
Journal or Publication Title: Journal of Mathematical Analysis and Applications
Uncontrolled Keywords: Linear spectral pencil ; Eigenvalue counting function ; Dirac operator ; Zero modes
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 58490
Deposited By: ep_importer_pure
Deposited On: 18 Sep 2012 12:30
Refereed?: Yes
Published?: Published
Last Modified: 31 Mar 2014 09:56
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/58490

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