Displaying similar documents to “Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian.”

Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields

Akira Iwatsuka, Hideo Tamura (1998)

Annales de l'institut Fourier

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This article studies the asymptotic behavior of the number N ( λ ) of the negative eigenvalues < - λ as λ → + 0 of the two dimensional Pauli operators with electric potential V ( x ) decaying at ∞ and with nonconstant magnetic field b ( x ) , which is assumed to be bounded or to decay at ∞ . In particular, it is shown that N ( λ ) = ( 1 / 2 π ) ∫ V ( x ) > λ b ( x ) d x ( 1 + o ( 1 ) ) , when V ( x ) decays faster than b ( x ) under some additional conditions.

Domain perturbations, capacity and shift of eigenvalues

André Noll (1999)

Journées équations aux dérivées partielles

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After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator H . If H is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in (, 24:759–775, 1999) and obtain a lower bound which leads to a generalization of Thirring’s inequality...