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Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients
Author(s) -
Simon Barry
Publication year - 2006
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20106
Subject(s) - mathematics , recursion (computer science) , spectrum (functional analysis) , unit circle , inverse , orthogonal polynomials , limit (mathematics) , pure mathematics , mathematical analysis , geometry , algorithm , physics , quantum mechanics
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. © 2005 Wiley Periodicals, Inc.