Best m-term trigonometric approximation of periodic functions of several variables from Nikol’skii–Besov classes for small smoothness

On $M$-Term Approximations of the Nikol'skii-Besov Class in the Lorentz Spaces

“…Temlyakov [20] follow from Theorem 1 -3. If 1 < p 2 < q < ∞ and m( 1 p − 1 q ) < r m p , the results of S.A. Stasyuk [16], [17] follow from the first and second items of Theorem 1.…”

“…Temlyakov [10], A.S. Romanyuk [11], Dinh Dung [12], Wang Heping and Sun Yongsheng [13], L. Q.Duan and G.S. Fang [14], W.Sickel and M. Hansen [15], S.A. Stasyuk [16], [17] and others (see bibliography in [18], [19], [20]).…”

On M-term approximations of the Nikolskii - Besov class

“…Temlyakov [9] follow from Theorem 2.1 -2.3. If 1 < p ≤ 2 < q < ∞ and m( 1 p − 1 q ) < r ≤ m p , the results of S.A. Stasyuk [20,21] follow from the first and second items of Theorem 2.1. Theorem 2.1 -2.3 were announced in [3].…”

“…Temlyakov [23], A.S. Romanyuk [19], Dinh Dung [10], D.B. Bazarkhanov [5], L. Duan [11], M. Hansen and W. Sickel [12], S.A. Stasyuk [20,21], and others (see bibliography in [1], [2], [8], [21], [23]).…”

Adaptive sampling recovery of functions with higher mixed regularity

“…We mention here only some papers of Hansen and Sickel [17], [18], [19], D. Dũng [5,6], Temlyakov [40,41], V. Romanyuk [30], [31] and Bazarkhanov [1], where the authors considered wavelet type dictionaries. Best n-term trigonometric approximation was studied by Temlyakov [44], [43], A. Romanyuk [25], [26], [27], [28], A. Romanyuk and V. Romanyuk [29], Stasyuk [38], [39] and others. Probably closest to us are the papers D. Dũng [7,9], where the univariate and isotropic framework is considered.…”