The infinite-dimensional widths and optimal recovery of generalized Besov classes
The purpose of the present paper is to consider some weak asymptotic problems concerning the infinite-dimensional Kolmogorov widths, the infinite-dimensional linear widths, the infinite-dimensional Gel'fand widths and optimal recovery in Besov space. It is obvious to be found that the results obtained and methods used in Besov space are easily generalized, and hence in this paper these results in an extension of Besov spaces on R-d are stated and proved. Meantime, the representation theorem and approximation of these spaces by polynomial splines are discussed. (C) 2002 Elsevier Science (USA).
infinite-dimensional width optimal recovery generalized besov classes