The \(N\)-width for a generalized periodic Besov classes (Q815127)

The author introduces generalised Besov spaces \(B^\Omega_{p \theta} (T^d)\) on the \(d\)-torus \(T^d\), where \(1\leq p, \theta \leq \infty\) and \(\Omega\), generated by a function \(\Omega (t)\), stands for a generalised smoothness, including \(\Omega (t) = t^\alpha\) for the classical Besov spaces, \(\alpha >0\). It is the main aim of the paper to determine the asymptotic behaviour of Kolmogorov widths, Gelfand widths and approximation numbers of the compact embedding of the unit ball in \(B^\Omega_{p \theta} (T^d)\) into \(L_q (T^d)\).