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

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

2004-12-16

arxiv.org/abs/math/0412336v1

Mathematics

Spectral Theory

Scientific paper

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.

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