Square-summable variation and absolutely continuous spectrum

  • Milivoje Lukic

    Rice University, Houston, USA


Recent results of Denisov [5] and Kaluzhny–Shamis [9] describe the absolutely continuous spectrum of Jacobi matrices with coefficients that obey an l2\mathcal l^2 bounded variation condition with step pp 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 p=1p=1 and p=2p=2, 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. 815–840

DOI 10.4171/JST/87