Finite Gap Jacobi Matrices, II. The Szegodouble acute Class - Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim (Constructive Approximation, 2011)
Let e ⊂ ℝ be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szegodouble acute condition is equivalent to (this includes prior results of Widom and Peherstorfer-Yuditskii). Using Remling's extension of the Denisov-Rakhmanov theorem and an analysis of Jost functions, we provide a new proof of Szegodouble acute asymptotics, including L2 asymptotics on the spectrum. We make heavy use of the covering map formalism of Sodin-Yuditskii as presented in our first paper in this series.
Keywords: Isospectral torus; Orthogonal polynomials; Szegodouble acute asymptotics