Bounded Variation

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  • orthogonal polynomials with recursion coefficients of generalized Bounded Variation
    Communications in Mathematical Physics, 2011
    Co-Authors: Milivoje Lukic
    Abstract:

    We consider probability measures on the real line or unit circle with Jacobi or Verblunsky coefficients satisfying an l p condition and a generalized Bounded Variation condition. This latter condition requires that a sequence can be expressed as a sum of sequences β (l), each of which has rotated Bounded Variation, i.e., $$\sum_{n=0}^\infty \vert e^{i\phi_l}\beta_{n+1}^{(l)} -\beta_n^{(l)}\vert < \infty$$ for some \({\phi_l}\) . This includes a large class of discrete Schrodinger operators with almost periodic potentials modulated by l p decay, i.e. linear combinations of \({\lambda_n {\rm cos}(2\pi\alpha n + \phi)}\) with \({\lambda \in \ell^p}\) of Bounded Variation and any α.