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On coincidence of classes of functions defined by the generalized modulus of smoothness and appropriate inverse theorem. (English) Zbl 1052.41517
Summary: We prove a theorem of coincidence of the class of functions defined by the generalized modulus of smoothness with the class of functions defined by the order of the best approximation by algebraic polynomials. We also prove the appropriate inverse theorem in approximation theory.
##### MSC:
 41A35 Approximation by operators (in particular, by integral operators) 41A50 Best approximation, Chebyshev systems 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series