Best \(m\)-term approximation and Sobolev-Besov spaces of dominating mixed smoothness -- the case of compact embeddings (Q443896)

In this paper, \(m\)-widths of tensor products of approximants separately from Sobolev and from Besov spaces are studied and asymptotically estimated, where the spaces are compactly embedded. The errors whose infima are taken are measured in the \(L_p\)-norm and the system from which the approximations are taken are tensor product wavelet systems with compactly supported wavelets and additional conditions on smoothness, moments and integrability. The principal general classes of function spaces which are used are the Besov-Lizorkin-Triebel spaces as those spaces which contain the mentioned Sobolev and Besov spaces (Chapter 3, and Chapter 5 for the associated sequence spaces) and the main theorems are summarised in Chapter 2. Among other things, the \(m\)-width results are also compared with best linear approximations and entropy numbers.