Abstract
We study the spectral properties of Jacobi matrices. By combining Killip's technique [12] with the technique of Killip and Simon [13] we obtain a result relating the properties of the elements of Jacobi matrices and the corresponding spectral measures. This theorem is a natural extension of a recent result of Laptev-Naboko-Safronov [17].
Note
The author thanks Sergei Naboko for useful discussions and Barry Simon for pointing out the conjecture.
Citation
Oleg Safronov. "The spectral measure of a Jacobi matrix in terms of the Fourier transform of the perturbation." Ark. Mat. 42 (2) 363 - 377, October 2004. https://doi.org/10.1007/BF02385486
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