OPUC的导数的L^2范数的渐近性
Asymptotics of the L^2 Norm of Derivatives of OPUC
摘要：
我们发现，对于许多家庭的OPUC，一个有$||φ'_n||_2/n -> 1$，我们称之为正常行为的条件。我们证明，这意味着$|α_n| -> 0$，它成立，如果序列$α_n$是在$\ell^1$。我们还证明了它是真实的许多稀疏序列。另一方面，它经常被质点的插入所破坏。
英文摘要：
We show that for many families of OPUC, one has $||φ'_n||_2/n -> 1$, a condition we call normal behavior. We prove that this implies $|α_n| -> 0$ and that it holds if the sequence $α_n$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
