Titlebook: Classification and Approximation of Periodic Functions; Alexander I. Stepanets Book 1995 Springer Science+Business Media Dordrecht 1995 Fo

Introduction

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https://doi.org/10.1007/978-3-662-47830-1In this chapter, we continue studying approximation by Fourier sums in the spaces . and . but, instead of the values .(.).(.) - .(.), we consider the linear combinations of the deviations .(ϕ.;.), where ϕ .(·), . 1,2, …,., are the derivatives of a function .(·) belonging to a given class.

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Reports of China’s Basic ResearchIn this chapter, we consider the values .of deviations of Fourier sums in the metric of the spaces . for functions from the classes ., where . is a certain subset in the space .. Most frequently, we take . = . = { ϕ;‖ ϕ ‖.≤1 } in this case, we set ..

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Introduction,It is well known for many years that every .π -periodic summable function .(.) can be associated in a one-to-one manner with its Fourier series ., where . and ..

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Simultaneous Approximation of Functions and their Derivatives by Fourier Sums,In this chapter, we continue studying approximation by Fourier sums in the spaces . and . but, instead of the values .(.).(.) - .(.), we consider the linear combinations of the deviations .(ϕ.;.), where ϕ .(·), . 1,2, …,., are the derivatives of a function .(·) belonging to a given class.

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Classification and Approximation of Periodic Functions

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Classification and Approximation of Periodic Functions978-94-011-0115-8

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