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Non-symmetric fast decreasing polynomials and applications. (English) Zbl 1254.41007
From the authors abstract: A polynomial ${P}_{n}$ is called fast decreasing if ${P}_{n}\left(0\right)=1$, and, on $\left[-1,1\right]$, ${P}_{n}$ decreases fast (in terms of $n$ and the distance from 0) as we move away from the origin. This paper considers the version in which ${P}_{n}$ decreases only on some non-symmetric interval $\left[-a,1\right]$ with possibly small $a$. In this case, one gets a faster decrease, and this type of extension is needed in some problems, when symmetric fast decreasing polynomials are not sufficient. Such non-symmetric fast decreasing polynomials are applied to find local bounds for Christoffel functions and for local zero spacing of orthogonal polynomials with respect to a doubling measure close to a local endpoint.
##### MSC:
 41A10 Approximation by polynomials
##### References:
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