Asymptotics for polynomials orthogonal in an indefinite metric

作者：Derevyagin Maxim^*; Simanek Brian

来源：Journal of Mathematical Analysis and Applications, 2018, 460(2): 777-793.

DOI：10.1016/j.jmaa.2017.12.038

• Orthogonal polynomials on the unit circle
• Pseudo-Caratheodory function
• Szego function
• Szego mapping
• Asymptotic
• Non-symmetric Jacobi matrix

We continue studying polynomials generated by the Szego recursion when a finite number of Verblunsky coefficients lie outside the closed unit disk. We prove some asymptotic results for the corresponding orthogonal polynomials and then translate them to the real line to obtain the Szego asymptotics for the resulting polynomials. The latter polynomials give rise to a non-symmetric tridiagonal matrix but it is a finite-rank perturbation of a symmetric Jacobi matrix.

• 出版日期2018-4-15