The Spectral Density of a Product of Spectral Projections
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چکیده
We consider the product of spectral projections Πε(λ) = 1(−∞,λ−ε)(H0)1(λ+ε,∞)(H)1(−∞,λ−ε)(H0) where H0 and H are the free and the perturbed Schrödinger operators with a short range potential, λ > 0 is fixed and ε → 0. We compute the leading term of the asymptotics of Tr f(Πε(λ)) as ε → 0 for continuous functions f vanishing sufficiently fast near zero. Our construction elucidates calculations that appeared earlier in the theory of “Anderson’s orthogonality catastrophe” and emphasizes the role of Hankel operators in this phenomenon.
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تاریخ انتشار 2015