dc.contributor.author Beckermann, B. dc.contributor.author Martínez-Finkelshtein, Andrei dc.contributor.author Rakhmanov, Evgenii A. dc.contributor.author Wielonsky, F. dc.date.accessioned 2012-08-03T09:42:29Z dc.date.available 2012-08-03T09:42:29Z dc.date.issued 2004 dc.identifier.issn 1089-7658 dc.identifier.uri http://hdl.handle.net/10835/1640 dc.description.abstract 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 related to the entropy integral. First, their asymptotic behavior is completely described for weights $w$ in the Bernstein class. Then, as for the entropy, we obtain asymptotic upper bounds for these two functionals when $w(x)$ belongs to the Szeg\H{o} class. In each case, we give conditions for these upper bounds to be attained. es_ES dc.language.iso en es_ES dc.source Journal of Mathematical Physics 45 (11), 4239-4254 (2004) es_ES dc.subject Análisis asintótico es_ES dc.subject Polinomios ortogonales es_ES dc.subject Variables aleatorias es_ES dc.title Asymptotic upper bounds for the entropy of orthogonal polynomials in the Szegő class. es_ES dc.type info:eu-repo/semantics/article es_ES dc.rights.accessRights info:eu-repo/semantics/openAccess es_ES
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