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dc.contributor.authorBeckermann, B.
dc.contributor.authorMartínez-Finkelshtein, Andrei
dc.contributor.authorRakhmanov, Evgenii A.
dc.contributor.authorWielonsky, F.
dc.date.accessioned2012-08-03T09:42:29Z
dc.date.available2012-08-03T09:42:29Z
dc.date.issued2004
dc.identifier.issn1089-7658
dc.identifier.urihttp://hdl.handle.net/10835/1640
dc.description.abstractWe 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.isoenes_ES
dc.sourceJournal of Mathematical Physics 45 (11), 4239-4254 (2004)es_ES
dc.subjectAnálisis asintóticoes_ES
dc.subjectPolinomios ortogonaleses_ES
dc.subjectVariables aleatoriases_ES
dc.titleAsymptotic upper bounds for the entropy of orthogonal polynomials in the Szegő class.es_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses_ES


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