Linear widths of the classes B p,θ Ω of periodic functions of many variables in the space L q

The best m-term approximations on generalized Besov classes MBq,θΩDuan1 2010Journal of Approximation Theory5000View full textAdd to dashboardCite

“…In 1997, Sun and Wang [13] introduced the Besov classes B Ω q,θ (T d ) by means of Ω (t), i.e., an extension of the Besov classes S r q,θ (T d ), which was introduced first by Amanov [1] and gave the asymptotic estimates for Kolmogorov n-widths of the classes under the condition Ω (t) = ω(t 1 · · · · · t d ), where ω(t) ∈ Ψ * l (i.e., a univariate function) and Ψ * l will be given below. In addition, in [12,4], Stasyuk and Fedunyk studied the Kolmogorov and linear widths of B Ω q,θ (T d ) for some values of parameters p, q, θ, respectively. In this paper, we will consider the best m-term approximation of generalized Besov classes M B Ω q,θ (T d ) under the condition Ω (t) = ω(t 1 · · · · · t d ), where ω(t) ∈ Ψ * l (i.e., a univariate function) with regard to orthogonal dictionaries and prove that the orthogonal basis U d which consists of trigonometric polynomials (shifts of the Dirichlet kernels) is nearly optimal among orthogonal dictionaries.…”