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Asymptotic upper bounds for the entropy of orthogonal polynomials in the Szegő class.
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 |