Theory of extremal problems and approximation theory. (Chinese. English summary) Zbl 0728.41016

Tikhomirov, V. M.

Adv. Math., Beijing 19, No. 4, 449-451 (1990).

Summary: The notion of average dimension for a linear space of functions defined on the whole real axis is introduced. On this basis the author puts forward some new idea of extending the notion of Kolmogorov’s N-widths to the case, when the approximating subspaces are of infinite dimension.

MSC:

41A46	Approximation by arbitrary nonlinear expressions; widths and entropy
41A65	Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Keywords:

average dimension; Kolmogorov’s N-widths