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

## 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: | Journal Article |
---|---|

Journal or Publication Title: | Journal of Mathematical Analysis and Applications |

Uncontrolled Keywords: | Linear spectral pencil ; Eigenvalue counting function ; Dirac operator ; Zero modes |

Subjects: | ?? qa ?? |

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: | 12 Apr 2018 00:18 |

Identification Number: | |

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

### Actions (login required)

View Item |