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

Official URL: http://dx.doi.org/10.1016/j.jmaa.2012.03.001

## 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 |
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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: | 27 Sep 2016 01:20 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/58490 |

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