ORTHOGONAL POLYNOMIALS WITH PERIODICALLY MODULATED RECURRENCE COEFFICIENTS IN THE JORDAN BLOCK CASE

We study orthogonal polynomials with periodically modulated recurrence coefficients when 0 lies on the hard edge of the spectrum of the corresponding periodic Jacobi matrix. In particular, we show that their orthogonality measure is purely absolutely continuous on a real half-line and purely discrete on its complement. Additionally, we provide the constructive formula for the density in terms of Tur & aacute;n determinants. Moreover, we determine the exact asymptotic behavior of the orthogonal polynomials. Finally, we study scaling limits of the Christoffel-Darboux kernel.