This article is cited in 6 papers

The Newton–Leibniz formula on Banach spaces and approximation of functions of an infinite-dimensional argument

A. V. Uglanov


Abstract: Properties of integrals over infinite-dimensional nonlinear manifolds are analyzed. A certain double averaging operation is introduced for functions on abstract separable Banach spaces; this operation leads to uniform approximation by smooth (in the Fréchet sense) functions in the case of spaces (and certain other cases).
Bibliography: 10 titles.

UDC: 517.98

MSC: Primary 28C20, 41A65, 46B20, 58B99; Secondary 28A15, 28B05, 58D20

Received: 22.10.1984

 English version: Mathematics of the USSR-Izvestiya, 1988, 30:1, 145–161

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