Recent results of Denisov  and Kaluzhny–Shamis  describe the absolutely continuous spectrum of Jacobi matrices with coefficients that obey an bounded variation condition with step and are asymptotically periodic. We extend these results to orthogonal polynomials on the unit circle. We also replace the asymptotic periodicity condition by the weaker condition of convergence to an isospectral torus and, for and , we remove even that condition.
Cite this article
Milivoje Lukic, Square-summable variation and absolutely continuous spectrum. J. Spectr. Theory 4 (2014), no. 4, pp. 815–840DOI 10.4171/JST/87