Approximation characteristics of the classes B p,θ Ω of periodic functions of many variables

Abstract

We obtain exact order estimates for the approximation of the classes B Ω p,θ of periodic functions of many variables in the space Lq by using operators of orthogonal projection and linear operators satisfying certain conditions.

Best Approximations and Kolmogorov and Trigonometric Widths of the Classes B Ω p,θ of Periodic Functions of Many Variables

“…Therefore, Theorem 1 supplements the results given in [1] concerning the best approximation of the classes B p,θ Ω by trigonometric polynomials with "numbers" of harmonics from "graded hyperbolic crosses" and the results given in [22] concerning the approximation of the classes B p,θ Ω by "graded hyperbolic" Fourier sums.…”

Best M-term trigonometric approximations of the classes $ B^{\Omega }_{{p,{\text{ $ \theta $ }}}} $ of periodic functions of many variables in the space L q

“…We estimate the second term on the right-hand side of (22) as follows: By analogy, substituting f x 2 ( ) and P x ( ) into (17), we verify that the following order inequality holds in the case θ = ∞ : …”

Estimates of the approximation characteristics of the classes B p,θ Ω of periodic functions of several variables with given majorant of mixed moduli of continuity

“…In our notation (up to absolute constants), the classes B Ω p,θ , 1 ≤ p ≤ ∞, are defined as follows (see, respectively, [7] and [5]): In what follows, we shall consider the classes B Ω p,θ defined by a function Ω(t) of special form; namely,…”