Widths of Besov classes of generalized smoothness on the sphere (Q432768)

The main aim of this paper is to obtain the asymptotic orders of the Kolmogorov, linear and Gelfand \(n\)\,-widths of the Besov spaces \(B_{p\theta}^{\Omega}({\mathbb S}^{d-1})\) of generalized smothness in the spaces \(L_q({\mathbb S}^{d-1})\) for all \(1\leq p,q \leq\infty\) as \(n\to\infty\). A corresponding representation theorem, an embedding theorem, and a characterization of the spaces \(B_{p\theta}^{\Omega}({\mathbb S}^{d-1})\) are also obtained.