Asymptotics of the L^2 Norm of Derivatives of OPUC

Details Asymptotics of the L^2 Norm of Derivatives of OPUC Asymptotics of the L^2 Norm of Derivatives of OPUC

2010-06-04

arxiv.org/abs/1006.0900v2

Mathematics

Classical Analysis and ODEs

36 pages, no figures. Minor corrections, to appear in the Journal of Approximation Theory

Scientific paper

We show that for many families of OPUC, one has $||\varphi'_n||_2/n -> 1$, a
condition we call normal behavior. We prove that this implies $|\alpha_n| -> 0$
and that it holds if the sequence $\alpha_n$ is in $\ell^1$. We also prove it
is true for many sparse sequences. On the other hand, it is often destroyed by
the insertion of a mass point.

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