Abstract:
A finite complex Borel measure μ on the unit circle or on the real line is called Rajchman if its Fourier coefficients tend to 0 as n→∞. In quantum dynamics the self-adjoint operators (Hamiltonians) whose spectral measures are Rajchman correspond to the systems having certain scattering properties. In this paper we study how a small perturbation of the operator can affect the Rajchman property of its spectral measure. Our approach is based on the notion of the local symmetry of measures.
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Received: 17 April 2001 / Accepted: 18 June 2001
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Poltoratski, A. Survival Probability¶in Rank-One Perturbation Problems. Commun. Math. Phys. 223, 205–222 (2001). https://doi.org/10.1007/s002200100541
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DOI: https://doi.org/10.1007/s002200100541