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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 (0)=1, and, on [-1,1], 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 [-a,1] 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.
41A10Approximation by polynomials
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