Abstract
The pseudorelativistic Hamiltonian \(G_{1/2} = (( - i\nabla - A)^2 + I)^{1/2} + W,x \in \mathbb{R}^d ,d \geqslant 2,\) is considered under wide conditions on potentials A(x), W(x). It is assumed that a real point λ is regular for G1/2. Let G1/2(α)=G1/2−αV, where α>0, V(x)≥0, and V ∈L d(ℝd). Denote by N(λ, α) the number of eigenvalues of G1/2(t) that cross the point λ as t increases from 0 to α. A Weyl-type asymptotics is obtained for N(λ, α) as α→∞. Bibliography: 5 titles.
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Additional information
To O. A. Ladyzhenskaya
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 249, 1997. pp. 102–117.
Translated by A. B. Pushnitskii.
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Birman, M.S., Pushnitskii, A.B. Discrete spectrum in the gaps of a perturbed pseudorelativistic hamiltonian. J Math Sci 101, 3437–3447 (2000). https://doi.org/10.1007/BF02680144
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DOI: https://doi.org/10.1007/BF02680144