Abstract
In this paper various transformations of trigonometrical polynomials are introduced; these are then used to deduce asymptotic formulas for the behavior of sequences of integrals of the moduli of the polynomials. As a consequence a definitive form is found for a relationship (in both directions) between the summability and absolute convergence of trigonometric Fourier series which has been noted earlier by the author.Bibliography: 26 titles.
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