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Best Trigonometric Approximation, Fractional Order Derivatives and Lipschitz Classes

Published online by Cambridge University Press:  20 November 2018

P. L. Butzer ,
H. Dyckhoff ,
E. Görlich  and
R. L. Stens
P. L. Butzer
Affiliation:
Technological University of Aachen, Aachen, West Germany
H. Dyckhoff
Affiliation:
Technological University of Aachen, Aachen, West Germany
E. Görlich
Affiliation:
Technological University of Aachen, Aachen, West Germany
R. L. Stens
Affiliation:
Technological University of Aachen, Aachen, West Germany
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Let C2π denote the space of 2π-periodic continuous functions and πn the set of trigonometric polynomials of degree ≦ n, where n ϵ P = {0, 1, … } . Given θ > 0, the well-known theorem of Stečkin and its converse state that the best approximation of an ƒ ϵ C2π with respect to the max-norm satisfies

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 781 - 793
Copyright
Copyright © Canadian Mathematical Society 1977

References

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