2011
DOI: 10.1007/s10474-011-0072-8
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On estimating the rate of best trigonometric approximation by a modulus of smoothness

Abstract: Best trigonometric approximation in Lp, 1 p ∞, is characterized by a modulus of smoothness, which is equivalent to zero if the function is a trigonometric polynomial of a given degree. The characterization is similar to the one given by the classical modulus of smoothness. The modulus possesses properties similar to those of the classical one.

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Cited by 3 publications
(6 citation statements)
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“…To verify the latter, we take into account that F r f = A r F with F = F r−1 f ; hence B r F r f = = B r A r F = F + η r * F with η r (x) = −1 − 2 cos rx as was established in [11] ((2.9)). Set G = F r f and let G t ∈ W 2r−1 p (T) satisfy (4.6), (4.7) for G in the place of F. Then…”
Section: Improved Relations Between Trigonometric Moduli Of Differentmentioning
confidence: 99%
See 3 more Smart Citations
“…To verify the latter, we take into account that F r f = A r F with F = F r−1 f ; hence B r F r f = = B r A r F = F + η r * F with η r (x) = −1 − 2 cos rx as was established in [11] ((2.9)). Set G = F r f and let G t ∈ W 2r−1 p (T) satisfy (4.6), (4.7) for G in the place of F. Then…”
Section: Improved Relations Between Trigonometric Moduli Of Differentmentioning
confidence: 99%
“…Set F = F r−1 f. Then F r f = F + r 2 a * F. In [11] (3.2) it was proved that (a * g) = g + const for any g ∈ L p (T). Then, using basic properties of the classical modulus, we get…”
Section: Improved Relations Between Trigonometric Moduli Of Differentmentioning
confidence: 99%
See 2 more Smart Citations
“…This notion could considered as direct generalization of classical trigonometric approximation in weighted space , ( ) and it is more natural to use it for number of problems of approximation functions ( see, for example [3], [5], [6], [9]). The important problem of approximation theory and theory of Fourier series is the problem of description of best approximation of functions by trigonometric polynomials see [7] and [10].One can consider this problem from the viewpoint of description of Roman Taberski of trigonometric approximation.…”
Section: Introductionmentioning
confidence: 99%