Abstract
Trigonometric approximation is considered in this chapter. We start this chapter with the Fourier operator and Fourier sums and give approximations by sums of Fourier and Fejér and de la Vallée Poussin means. Their discrete versions and the Lagrange trigonometric operator are also investigated. As a basic tool for studying approximating properties of the Lagrange and de la Vallée Poussin operators we consider the so-called Marcinkiewicz inequalities. Beside the uniform approximation we also investigate the Lagrange interpolation error in Lp-norm (1<p<+∞) and give some estimates of the interpolation errors in the L1-Sobolev norm. Finally, we give the weighted versions of some of the results stated in the previous sections.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Trigonometric Approximation. In: Interpolation Processes. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68349-0_3
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DOI: https://doi.org/10.1007/978-3-540-68349-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68346-9
Online ISBN: 978-3-540-68349-0
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