Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case (Q6567987)

In this nice contribution, the authors consider orthogonal polynomials with periodically modulated recurrence coefficients when 0 lies on the hard edge of the spectrum of the corresponding periodic Jacobi matrix. They establish that their orthogonality measure is purely absolutely continuous on a real half-line and purely discrete on its complement. Also, they highlight the constructive formula for the density in terms of Turán determinants and the exact asymptotic behavior of the orthogonal polynomials. Moreover, they study the scaling limits of the Christoffel-Darboux kernel.