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Zapiski Nauchnykh Seminarov LOMI, 1979, Volume 92, Pages 60–84
(Mi znsl3190)
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This article is cited in 1 scientific paper (total in 1 paper)
The simultaneous approximation by polynomials on the circle and in the interior of the disc
A. L. Vol'berg
Abstract:
The subject of this paper is the investigation of the question whether the polynomials form a dense set in the space $L^2(h)\oplus L^2(\mu_{\mathbb D})$ where $h$ is a weight on the unit circle $\mathbb T$ and $\mu_{\mathbb D}$ is a measure in the unit disc $\mathbb D$. In the case $\operatorname{supp}\mu_{\mathbb D}\subset[0,1]$ some necessary and some (close) sufficient conditions for the answer to be positive are obtained (these conditions say, roughly speaking, thet the functions
$\mu_{\mathbb D}(1-\delta,1)$ and $h(e^{i\Theta})$ tend to zero sufficiently rapidly as $\delta\to0$ and $\Theta\to0$). In the general case only sufficient conditions are given.
Citation:
A. L. Vol'berg, “The simultaneous approximation by polynomials on the circle and in the interior of the disc”, Investigations on linear operators and function theory. Part IX, Zap. Nauchn. Sem. LOMI, 92, "Nauka", Leningrad. Otdel., Leningrad, 1979, 60–84
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https://www.mathnet.ru/eng/znsl3190 https://www.mathnet.ru/eng/znsl/v92/p60
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Abstract page: | 317 | Full-text PDF : | 95 |
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