Abstract
Order-sharp estimates are established for the best N-term approximations of functions from Nikol’skii–Besov type classes B pq sm(Tk) with respect to the multiple trigonometric system T(k) in the metric of L r (Tk) for a number of relations between the parameters s, p, q, r, and m (s = (s 1,..., s n ) ∈ R+ n, 1 ≤ p, q, r ≤ ∞, m = (m 1,..., m n ) ∈ Nn, k = m 1 +... + m n ). Constructive methods of nonlinear trigonometric approximation—variants of the so-called greedy algorithms—are used in the proofs of upper estimates.
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Original Russian Text © D.B. Bazarkhanov, 2016, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 293, pp. 8–42.
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Bazarkhanov, D.B. Nonlinear trigonometric approximations of multivariate function classes. Proc. Steklov Inst. Math. 293, 2–36 (2016). https://doi.org/10.1134/S0081543816040027
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DOI: https://doi.org/10.1134/S0081543816040027