On multivariate adaptive approximation (Q1581106)

The authors prove several interesting results, using the modified adaptive approximation introduced by A. Cohen, R. A. De Vore, P. Petrushev and H. Xu in the space \(BV(\mathbb{R}^2)\). They also show that the new modified adaptive approximation generates near-minimizers to some extremal problems in the spaces \(V^r_{\sigma,p} (\mathbb{R})\) of functions of ``bounded variation'' and Besov spaces \(B^\alpha (\mathbb{R}^d)\), too.