Abstract
The following result is proved: if approximations in the norm of (of ) of functions in the classes (in , respectively) by some linear operators have the same order of magnitude as the best approximations, then the set of norms of these operators is unbounded. Also Bernstein's and the Jackson-Nikol'skiǐ inequalities are proved for trigonometric polynomials with spectra in the sets (in ).Bibliography: 15 titles.
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