Asymptotics of the L-2 norm of derivatives of OPUC

作者：Martinez Finkelshtein Andrei; Simon Barry^*

来源：Journal of Approximation Theory, 2011, 163(6): 747-778.

DOI：10.1016/j.jat.2010.09.002

• Orthogonal polynomials
• Derivative asymptotics

We show that for many families of OPUC, one has parallel to phi(n)'parallel to(2)/n -> 1, a condition we call normal behavior. We prove that this implies vertical bar alpha(n)vertical bar -> 0 and that it holds if Sigma(infinity)(n=0) vertical bar alpha(n)vertical bar < infinity. 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.

• 出版日期2011-6