Abstract
Assume that f(x) is a given function and we are going to approximate it by a sequence of functions F n (f,x). Let δ n (x)= δ n (f,F n ,x) =f(x)-F n (f,x). If F n (f,x) is a polynomial, then the value δ n (x) can often be represented as a convolution where the function ϕ depends only on f, and the kernel Φ n depends only on a method of constructing operators F n (x). This forms a basis of one of the most widely used and efficient approaches to studying the value δ n (x), which is finally reduced to investigating sequences of integral operators.
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© 1995 Springer Science+Business Media Dordrecht
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Stepanets, A.I. (1995). Integral Representations of Deviations of Linear Means of Fourier Series. In: Classification and Approximation of Periodic Functions. Mathematics and Its Applications, vol 333. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0115-8_3
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DOI: https://doi.org/10.1007/978-94-011-0115-8_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4055-6
Online ISBN: 978-94-011-0115-8
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