Trigonometric Widths and Best N-Term Approximations of the Generalized Periodic Besov Classes B_(p,θ)~Ω

In this paper,we determine the estimates exact in order for the trigonometric widths and the best n-term trigonometric approximations of the generalized classes of periodic functions B(p,θ)Ω in the space Lq for some values of parameters p,q.     

Trigonometric Widths of the Classes B p,θ Ω of Periodic Functions of Many Variables

We obtain exact order estimates for the trigonometric widths of the classes of periodic functions of many variables in the space L _q, 1 < p 2 q < p/(p – 1).     

Best M-Term Trigonometric Approximations of the Classes B p,θ Ω of Functions of Many Variables

We obtain exact order estimates for the best M-term trigonometric approximations of the classes B _p, of functions of many variables in the space L _q, 1 < p < q < , q > 2.     

Widths of the Besov Classes B p,θ r(Td)

Mathematical Notes - In this paper we obtain estimates of the orders of Kolmogorov widths of the Besov classes B p,θ r(Td of periodic functions of several variables with dominant mixed...     

Estimates of the Best M-Term Trigonometric Approximations of the Classes Lβ, pψ of Periodic Functions of Many Variables in the Space Lq

We obtain order estimates for the best trigonometric approximations of the classes L _{, p} of periodic functions of many variables in the space L _q for 1 < p < q 2 and 1 < q p < .     

Best Orthogonal Trigonometric Approximations of Classes of Functions of Many Variables Lβ, pψ

We obtain order estimates for the best orthogonal trigonometric approximations of classes of functions of many variables L _{, p} in the space L _q, 1 < p < q < , q > 2.     

Approximation of Classes B p,θ r by Linear Methods and Best Approximations

We investigate problems related to the approximation by linear methods and the best approximations of the classes , 1 p in the space L .     

Trigonometric Widths of the Classes L β,p Ψ of Functions of Many Variables

We obtain order estimates for the trigonometric widths of the classes L _,p of periodic functions of many variables in the space L _q for 1 < p 2 q < p/(p – 1).     

N-Widths and Average Widths of Besov Classes in Sobolev Spaces

In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively.     

Kolmogorov Widths of the Nikol’skii–Besov Classes of Periodic Functions of Many Variables in the Space of Quasicontinuous Functions

Ukrainian Mathematical Journal - We obtain order estimates for the M-dimensional Kolmogorov widths of the Nikol’skii–Besov classes of periodic functions of many variables with...     

The Average Widths of Sobolev-Wiener Classes and Besov-Wiener Classes

This paper concerns the problem of average σ-width of Sobolev-Wiener classes W^rpq(R^d),W^rpq(M,R^d),and Besov-Wiener classes S^rpqθb(R^d).S^rpqθB(R^d),S^rpqθb(M,R^d),S^rpqθB(R^d)in the metric Lq(R^d) for 1≤q≤p≤∞.The weak asymptotic results concerning the average linear widths,the average Bernstein widths and the infinite-dimensional Gel‘fand widths are obtained,respectively.     

Estimates for Approximation Characteristics of the Besov Classes B r p,θ of Periodic Functions of Many Variables in the Space Lq. I

We obtain order estimates for the approximation of the classes B _r ^p, of periodic functions of many variables in the space L _q by using operators of orthogonal projection and linear operators satisfying certain conditions.     

Approximation of the Classes B p,θ Ω of Periodic Functions of Many Variables in Uniform Metric

We obtain order estimates for the best M-term trigonometric approximations and approximations by Fourier sums for the classes B _p, of periodic functions of many variables in the uniform metric.     

The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness

The classes of the multivariate functions with bounded moduli on Rd and Td are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the corresponding quantities.     

Generalized Smoothness and Approximation of Periodic Functions in the Spaces Lp, 1 < p < +∞

Mathematical Notes - Norms of images of operators of multiplier type with an arbitrary generator are estimated by using best approximations of periodic functions of one variable by trigonometric...     

On the Best Polynomial Approximations of 2π-Periodic Functions and Exact Values of n-Widths of Functional Classes in the Space L 2

To solve extremal problems of approximation theory in the space L ₂, we use -moduli introduced by Ivanov. We determine the exact values of constants in Jackson-type inequalities and the exact values of n-widths of functional classes determined by these moduli.