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Inequalities for Trigonometric Polynomials and Some Integral Means

✍ Scribed by Hans-Bernd Knoop; Xinlong Zhou

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
122 KB
Volume
255
Category
Article
ISSN
0022-247X

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✦ Synopsis

Some inequalities associated with the Laplacian for trigonometric polynomials are given, which will be applied to investigate the behavior in approximation by trigonometric polynomials in higher dimensions and the best lower and upper estimates for some linear operators. In particular, we obtain a complete characterization for the approximation behavior of the classical Jackson operator. Thus the approximation error of a function by Jackson polynomials is equivalent to a K-functional defined by the Laplacian.

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