A remark on the trigonometric system
Abstract
We present a new property of the trigonometric system arranged in a natural order. It is shown that the sequence of subspaces of trigonometric polynomials is optimal in the sense of order of convergence on convolution classes K*Up in Lq for any 1<p,q<∞ just in the cases of "very slow" or "very fast" rate of decay of Fourier coefficients of K.
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