abstract:
It is wellknown that isotropic Besov spaces can be characterized by wavelets. Probably less wellknown are those function spaces which are characterized by tensor product wavelet systems. Specific examples are certain tensor products of Besov spaces.
We shall discuss the quality of best mterm approximation with respect to these two examples, i.e., Besov spaces and tensor products of Besov spaces. More exactly, we shall investigate the asymptotic behaviour of the widths of best mterm approximation, here denoted by σ_m(Y,X,Φ).
In our lectures, usually X = Lp(Ω), Φ denotes the wavelet system and Y will be either an isotropic Besov space or a tensor product Besov space. Our approach relies on the abstract theory of approximation spaces which we will shortly recall. Methods from interpolation theory (in particular real interpolation) will also play a role. We shall spend some time to discuss the similarities as well as the differences between the isotropic and the tensor product situation.
Finally, we shall compare best mterm approximation with optimal linear approximation. For this purpose we shall also introduce and discuss a few properties of approximation numbers (linear widths).
