Asymptotic upper bounds for the entropy of orthogonal polynomials in the Szegő class.
We give an asymptotic upper bound as $n\to\infty$ for the entropy integral $$E_n(w)= -\int p_n^2(x)\log (p_n^2(x))w(x)dx,$$ where $p_n$ is the $n$th degree orthonormal polynomial with respect to a weight $w(x)$ on $[-1,1]$ which belongs to the Szeg\H{o} class. We also study two functionals closely r...
| Main Authors: | , , , |
|---|---|
| 格式: | info:eu-repo/semantics/article |
| 語言: | English |
| 出版: |
2012
|
| 主題: | |
| 在線閱讀: | http://hdl.handle.net/10835/1640 |