Oleg Safronov The spectral measure of a Jacobi matrix in terms of the Fourier transform of the perturbation (131K, Postscript) ABSTRACT. We study the spectral properties of Jabobi matrices. By combining Killip's technique \cite{13} with the technique of Killip and Simon \cite{12} 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 \ctite{17}