The Szegő condition for Coulomb Jacobi matrices Original Research Article

A Jacobi matrix with an→1, bn→0 and spectral measure ν′(x) dx+dνsing(x) satisfies the Szegő condition if∫0πln[ν′(2 cos θ)] dθis finite. We prove that ifan≡1+αn+O(n−1−ε), bn≡βn+O(n−1−ε)with 2α⩾|β| and ε>0, then the corresponding matrix is Szegő.