Abstract
Order-sharp estimates of the best orthogonal trigonometric approximations of the Nikol’skii-Besov classes Bp,θr of periodic functions of several variables in the space Lq are obtained. Also the orders of the best approximations of functions of 2d variables of the form g(x, y) = f(x−y), x, y ∈ \(\mathbb{T}\)d = Πj=1d[−π, π], f(x) ∈ Bp,θr, by linear combinations of products of functions of d variables are established.
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