Abstract :
We obtain the continuous analogs of Rakhmanovʹs Theorem for polynomials orthogonal on the unit circle. Sturm–Liouville operators and Krein systems are considered. For a Sturm–Liouville operator with bounded potential q, we prove the following statement. If the essential spectrum and absolutely continuous component of the spectral measure fill the whole positive half-line, then q decays at infinity in the certain integral sense.
