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This article is cited in 14 scientific papers (total in 14 papers)
The asymptotic behavior of orthogonal polynomials
V. M. Badkov
Abstract:
Let $\{\varphi_{\sigma,n}(z)\}_{n=0}^\infty$ be the system of polynomials orthonormal on the unit circumference with respect to the measure $\sigma$. By way of generalizing and strengthening a number of previous results, we show that if $\ln\sigma'(\theta)\in L^1[0,2\pi]$,
$\sigma'(\theta)$ continuous and positive on $[a,b]\subset[0,2\pi]$, and $\omega(\sigma';\tau)_{[a,b]}\tau^{-1}\in L^1[0,b-a]$, then the
polynomials $\varphi_{\sigma,n}^*(e^{i\theta})=e^{in\theta}\overline{\varphi_{\sigma,n}(e^{i\theta})}$ converge uniformly in $\theta$, inside $(a,b)$, to the Szegö function. The result so formulated is shown to be definitive.
Bibligraphy: 16 titles.
Received: 03.08.1978
Citation:
V. M. Badkov, “The asymptotic behavior of orthogonal polynomials”, Mat. Sb. (N.S.), 109(151):1(5) (1979), 46–59; Math. USSR-Sb., 37:1 (1980), 39–51
Linking options:
https://www.mathnet.ru/eng/sm2353https://doi.org/10.1070/SM1980v037n01ABEH001941 https://www.mathnet.ru/eng/sm/v151/i1/p46
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Abstract page: | 434 | Russian version PDF: | 127 | English version PDF: | 20 | References: | 51 |
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