ar X iv : 0 90 6 . 16 30 v 1 [ m at h . SP ] 9 J un 2 00 9 FINITE GAP JACOBI MATRICES , II . THE SZEGŐ CLASS
نویسندگان
چکیده
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 Szeg˝ o condition is equivalent to lim sup a 1 · · · a n cap(e) n > 0 (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 Szeg˝ o asymptotics, including L 2 asymptotics on the spectrum. We use heavily the covering map formalism of Sodin–Yuditskii as presented in our first paper in this series.
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