On the nonclassical approximation method for periodic functions by trigonometric polynomials

We study the approximation of functions by linear polynomial means of their Fourier series with a function-multiplier φ that is equal to 1 not only at zero, in contrast with classical methods of summability. The exact order of convergence to zero of the sequence ( Fourier coefficients) as n→∞ is obt...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2013-01, Vol.188 (2), p.113-127
Main Authors: Kolomoitsev, Yurii S., Trigub, Roald M.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We study the approximation of functions by linear polynomial means of their Fourier series with a function-multiplier φ that is equal to 1 not only at zero, in contrast with classical methods of summability. The exact order of convergence to zero of the sequence ( Fourier coefficients) as n→∞ is obtained. The answer is given in terms of the values of difference operators of a continuous function f and a special K -functional (step of ). In addition, we obtain not only the sufficient conditions for φ but the necessary ones as well.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-012-1111-x