Abstracts
For a continuous 2π-periodic real-valued functionf, we investigate the asymptotic behavior of the zeros of the errorf(θ)−s n (θ), wheres n (θ) is thenth Fourier section. We prove that there is a subsequence {n k } for which such zeros (interpolation points) are uniformly distributed on [−π, π]. This extends previous results of Saff and Shekhtman. Moreover, results dealing with the maximal distance between consecutive zeros off−s n k are obtained. The technique of proof involves coefficient estimates for lacunary trigonometric polynomials in terms of itsL q -norm on a subinterval.
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Communicated by Vilmos Totik.
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Binev, P., Petrushev, P., Saff, E.B. et al. Distribution of interpolation points of bestL 2-approximants (nth partial sums of Fourier series). Constr. Approx 9, 445–472 (1993). https://doi.org/10.1007/BF01204651
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DOI: https://doi.org/10.1007/BF01204651