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Shannon entropy of symmetric Pollaczek polynomials
dc.contributor.author | Martínez Finkelshtein, Andrei | |
dc.contributor.author | Sánchez-Lara, J. F. | |
dc.date.accessioned | 2012-08-03T08:25:59Z | |
dc.date.available | 2012-08-03T08:25:59Z | |
dc.date.issued | 2007 | |
dc.identifier.uri | http://hdl.handle.net/10835/1635 | |
dc.description.abstract | We discuss the asymptotic behavior (as $n\to \infty$) of the entropic integrals $$ E_n= - \int_{-1}^1 \log \big(p^2_n(x) \big) p^2_n(x) w(x) d x, $$ and $$ F_n = -\int_{-1}^1 \log (p_n^2(x)w(x)) p_n^2(x) w(x) dx, $$ when $w$ is the symmetric Pollaczek weight on $[-1,1]$ with main parameter $\lambda\geq 1$, and $p_n$ is the corresponding orthonormal polynomial of degree $n$. It is well known that $w$ does not belong to the Szeg\H{o} class, which implies in particular that $E_n\to -\infty$. For this sequence we find the first two terms of the asymptotic expansion. Furthermore, we show that $F_n \to \log (\pi)-1$, proving that this ``universal behavior'' extends beyond the Szeg\H{o} class. The asymptotics of $E_n$ has also a curious interpretation in terms of the mutual energy of two relevant sequences of measures associated with $p_n$'s. | es_ES |
dc.language.iso | en | es_ES |
dc.source | Journal of Approximation Theory Vol. 145 Nº 1 (2007) | es_ES |
dc.subject | Polinomios simétricos Pollaczek | es_ES |
dc.subject | Entropía de Shannon | es_ES |
dc.subject | Comportamiento asintótico | es_ES |
dc.subject | Integrales entrópicas | es_ES |
dc.subject | Shannon entropy | es_ES |
dc.subject | Symmetric Pollaczek polynomials | es_ES |
dc.subject | Asymptotic behavior | es_ES |
dc.subject | Entropic integrals | es_ES |
dc.title | Shannon entropy of symmetric Pollaczek polynomials | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |