Fine structure of the zeros of orthogonal polynomials, III. Periodic recursion coefficients

2004/12/16 by Barry Simon, Simon, Barry · 1 citation
Mathematics · #35Q58 #FOS: Mathematics #Primary 26C10 #Secondary 48J53 #Spectral Theory (math.SP) #math.SP #msc:26C10 #msc:35Q58 #msc:48J53

paper · pdf · doi:10.48550/arxiv.math/0412336

arxiv created 2004/12/16 · arxiv updated 2009/12/01

Abstract

We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolutely continuous spectrum have a clock structure with spacings inverse to the density of zeros. Zeros away from the a.c. spectrum have limit points mod p and only finitely many of them.

Cited by

• Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients

Related

• On the zeros of orthogonal polynomials on the unit circle
• Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two Pictures
• Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients
• Fine Structure of the Zeros of Orthogonal Polynomials, IV. A Priori Bounds and Clock Behavior
• Orthogonal polynomials with periodic recurrence coefficients