Representation and approximation of multivariate periodic functions with bounded mixed moduli of smoothness. (English) Zbl 1032.42015
Proc. Steklov Inst. Math. 219, 350-371 (1997) and Tr. Mat. Inst. Steklova 219, 356-377 (1997).
The authors introduce the Besov class \(B^\Omega_{q,\theta}(\pi_d)\) as an extension of the class \(S^r_{q,\theta}(\pi_d)\) investigated by T. I. Amanov [Proc. Steklov Inst. Math. 77, 3-36 (1965); translation from Tr. Mat. Inst. Steklova 77, 5-34 (1965; Zbl 0152.12701)], and prove representation theorems for this class, approximation theorems on approximation of functions from \(B^\Omega_{q,\theta}(\pi_d)\) by Fourier sums of hyperbolic-cross type and asymptotic estimates of the Kolmogorov \(N\)-width \(d_N(B^\Omega_{q,\theta}, L_p)\).
For the entire collection see [Zbl 0907.00017].
For the entire collection see [Zbl 0907.00017].
Reviewer: W.Łenski (Poznań)
MSC:
| 42B05 | Fourier series and coefficients in several variables |
| 41A46 | Approximation by arbitrary nonlinear expressions; widths and entropy |
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
