This article is cited in 9 papers

On classes of infinitely differentiable functions

P. L. Ul'yanov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Sharp estimates are established for the relationships among the rate of growth of the derivatives of an infinitely-differentiable periodic function, the behavior of its Fourier coefficients, and the trigonometric polynomials of best approximation to it.

UDC: 517.5

MSC: Primary 42A10, 42A16; Secondary 42A05, 41A17

Received: 23.11.1989

 English version: Mathematics of the USSR-Sbornik, 1991, 70:1, 11–30

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