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Constructive Approximation - Let E = [–1, α] \cup [β, 1], –1 &;lt; α &;lt; β &;lt; 1, and let (pn) be orthogonal on E with respect to the weight function... 相似文献
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In this paper the distribution of the zeros of the error function for bestL
1-approximation by rational functions fromR
n,m
is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff. 相似文献
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F. Peherstorfer 《Constructive Approximation》1997,13(2):261-269
We give explicitly a class of polynomials with complex coefficients of degreen which deviate least from zero on [−1, 1] with respect to the max-norm among all polynomials which have the same,m + 1, 2m ≤n, first leading coefficients. Form=1, we obtain the polynomials discovered by Freund and Ruschewyh. Furthermore, corresponding results are obtained with respect
to weight functions of the type 1/√ρl, whereρl is a polynomial positive on [−1, 1]. 相似文献
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F. Peherstorfer 《Constructive Approximation》1996,12(2):161-185
Let (P ν) be a sequence of monic polynomials orthogonal on the unit circle with respect to a nonnegative weight function, let (Ωυ) the monic associated polynomials of (P v), and letA andB be self-reciprocal polynomials. We show that the sequence of polynomials (APυλ+BΩυλ)/Aλ, λ stuitably determined, is a sequence of orthogonal polynomials having, up to a multiplicative complex constant, the same recurrence coefficients as theP ν's from a certain index value onward, and determine the orthogonality measure explicity. Conversely, it is also shown that every sequence of orthogonal polynomials on the unit circle having the same recurrence coefficients from a certain index value onward is of the above form. With the help of these results an explicit representation of the associated polynomials of arbitrary order ofP ν and of the corresponding orthogonality measure and Szegö function is obtained. The asymptotic behavior of the associated polynomials is also studied. Finally necessary and suficient conditions are given such that the measure to which the above introduced polynomials are orthogonal is positive. 相似文献
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Franz Peherstorfer Peter Yuditskii 《Proceedings of the American Mathematical Society》2001,129(11):3213-3220
Let be a positive measure whose support is an interval plus a denumerable set of mass points which accumulate at the boundary points of only. Under the assumptions that the mass points satisfy Blaschke's condition and that the absolutely continuous part of satisfies Szegö's condition, asymptotics for the orthonormal polynomials on and off the support are given. So far asymptotics were only available if the set of mass points is finite.
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F. Peherstorfer 《Constructive Approximation》1996,12(4):481-488
LetW N(z)=aNzN+... be a complex polynomial and letT n be the classical Chebyshev polynomial. In this article it is shown that the polynomials (2aN)?n+1Tn(WN), n ∈N, are minimal polynomials on all equipotential lines for {z∈C:|W N(z)|≤1 Λ ImW N(z)=0} 相似文献
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