On Rakhmanov ’ S Theorem for Jacobi Matrices

  title={On Rakhmanov ’ S Theorem for Jacobi Matrices},
  author={Sergey A. Denisov},
We prove Rakhmanov’s theorem for Jacobi matrices without the additional assumption that the number of bound states is finite. This result solves one of Nevai’s open problems. Consider a measure dμ with bounded support in R. Assume that it has infinitely many growth points. Let {pk} (k = 0, 1, . . .) be the system of polynomials orthonormal with respect to that measure, i.e., ∞ ∫ −∞ pk(x)pm(x)dμ(x) = δk,m, deg pl(x) = l. It is known [1] that the following recurrence relations hold: (1) b−1p0(x… CONTINUE READING