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

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)
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