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On the Measure of Approximation for Some Linear Means of Trigonometric Fourier Series

✍ Scribed by Andi Kivinukk

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
938 KB
Volume
88
Category
Article
ISSN
0021-9045

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✦ Synopsis

Many approximation methods in C 2? may be generated via a certain function . # C [0, 1] with .(0)=1, .(1)=0. The function . j (t)=cos( j&1Â2) ?t ( j # N) generates the Rogosinski approximation method [N. K. Bari, ``A Treatise on Trigonometric Series,'' Vols. I, II, Pergamon Press, New York, 1964]. Our idea consists in representing . by the orthogonal system . j to extend results previously known for the Rogosinski method to arbitrary approximation methods. We illustrate this by proving two asymptotic estimates for the measure of approximation.

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## Abstract The degree of pointwise approximation in the strong sense of 2π‐periodic functions from __L^p^__ (__p__ = (1 + α)^−1^, α > −1/2) is examined. An answer to the modified version of Leindler's problem [4] is given.