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...
Egile Nagusiak: | Beckermann, B., Martínez-Finkelshtein, Andrei, Rakhmanov, Evgenii A., Wielonsky, F. |
---|---|
Formatua: | info:eu-repo/semantics/article |
Hizkuntza: | English |
Argitaratua: |
2012
|
Gaiak: | |
Sarrera elektronikoa: | http://hdl.handle.net/10835/1640 |
Antzeko izenburuak
-
Computation of the entropy of polynomials orthogonal on an interval.
nork: Buyarov, V., et al.
Argitaratua: (2012) -
Orthogonality of Jacobi polynomials with general parameters.
nork: Kuijlaars, A. B. J., et al.
Argitaratua: (2012) -
Discrete entropies of orthogonal polynomials
nork: Aptekarev, A. I., et al.
Argitaratua: (2012) -
On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials
nork: Martínez-Finkelshtein, Andrei, et al.
Argitaratua: (2012) -
Strong asymptotics for Jacobi polynomials with varying nonstandard parameters.
nork: Kuijlaars, A. B. J., et al.
Argitaratua: (2012)