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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Eigenvalue counting estimates for a class of linear spectral pencils with applications to zero modes. / Elton, Daniel; Ta, Tri Ngoc.
In: Journal of Mathematical Analysis and Applications, Vol. 391, No. 2, 15.07.2012, p. 613-618.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Elton, D & Ta, TN 2012, 'Eigenvalue counting estimates for a class of linear spectral pencils with applications to zero modes', Journal of Mathematical Analysis and Applications, vol. 391, no. 2, pp. 613-618. https://doi.org/10.1016/j.jmaa.2012.03.001

APA

Elton, D., & Ta, T. N. (2012). Eigenvalue counting estimates for a class of linear spectral pencils with applications to zero modes. Journal of Mathematical Analysis and Applications, 391(2), 613-618. https://doi.org/10.1016/j.jmaa.2012.03.001

Vancouver

Elton D, Ta TN. Eigenvalue counting estimates for a class of linear spectral pencils with applications to zero modes. Journal of Mathematical Analysis and Applications. 2012 Jul 15;391(2):613-618. doi: 10.1016/j.jmaa.2012.03.001

Author

Elton, Daniel ; Ta, Tri Ngoc. / Eigenvalue counting estimates for a class of linear spectral pencils with applications to zero modes. In: Journal of Mathematical Analysis and Applications. 2012 ; Vol. 391, No. 2. pp. 613-618.

Bibtex

@article{d1d9bebb4c754d3cb368a4e4d5445954,
title = "Eigenvalue counting estimates for a class of linear spectral pencils with applications to zero modes",
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| 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.",
keywords = "Linear spectral pencil, Eigenvalue counting function , Dirac operator , Zero modes",
author = "Daniel Elton and Ta, {Tri Ngoc}",
year = "2012",
month = jul,
day = "15",
doi = "10.1016/j.jmaa.2012.03.001",
language = "English",
volume = "391",
pages = "613--618",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - Eigenvalue counting estimates for a class of linear spectral pencils with applications to zero modes

AU - Elton, Daniel

AU - Ta, Tri Ngoc

PY - 2012/7/15

Y1 - 2012/7/15

N2 - 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| 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.

AB - 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| 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.

KW - Linear spectral pencil

KW - Eigenvalue counting function

KW - Dirac operator

KW - Zero modes

U2 - 10.1016/j.jmaa.2012.03.001

DO - 10.1016/j.jmaa.2012.03.001

M3 - Journal article

VL - 391

SP - 613

EP - 618

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -