Nonlinear trigonometric approximations of multivariate function classes - Bazarkhanov, D. B. (Proceedings of the Steklov Institute of Mathematics, 2016)
Order-sharp estimates are established for the best N -term approximations of functions from Nikol’skii–Besov type classes B pq sm (T k ) with respect to the multiple trigonometric system T ( k ) in the metric of L r (T k ) 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 ) ∈ N n , 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.