Abstract
We propose a new method for estimating functionals in terms of higher order moduli of continuity with explicit constants. Using this method, we estimate deviations of linear methods of approximation by entire functions of finite degree and, in particular, by trigonometric polynomials. For illustration of the results, we derive estimates for the Riesz and Akhiezer–Krein–Favard averages. Bibliography: 14 titles.
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