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

Research output: Contribution to journalJournal article


<mark>Journal publication date</mark>15/07/2012
<mark>Journal</mark>Journal of Mathematical Analysis and Applications
Issue number2
Number of pages6
Pages (from-to)613-618
<mark>Original language</mark>English


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.