Ebook: Classification and Approximation of Periodic Functions

This monograph proposes a new classification of periodic functions, based on the concept of generalized derivative, defined by introducing multiplicators and shifts of the argument into the Fourier series of the original function. This approach permits the classification of a wide range of functions, including those of which the Fourier series may diverge in integral metric, smooth functions, and infinitely differentiable functions, including analytical and entire ones. These newly introduced classes are then investigated using the traditional problems of the theory of approximation. The results thus obtained offer a new way to look at classical statements for the approximation of differentiable functions, and suggest possibilities to discover new effects.
Audience: valuable reading for experts in the field of mathematical analysis and researchers and graduate students interested in the applications of the theory of approximation and Fourier series.

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Content:
Front Matter....Pages i-x
Introduction....Pages 1-4
Classes of Periodic Functions....Pages 5-41
Integral Representations of Deviations of Linear Means of Fourier Series....Pages 43-79
Approximations by Fourier Sums in the Spaces c and L 1 ....Pages 81-208
Simultaneous Approximation of Functions and their Derivatives by Fourier Sums....Pages 209-254
Convergence Rate of Fourier Series and Best Approximations in the Spaces L p ....Pages 255-304
Best Approximations in the Spaces C and L ....Pages 305-345
Back Matter....Pages 347-366

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Content:
Front Matter....Pages i-x
Introduction....Pages 1-4
Classes of Periodic Functions....Pages 5-41
Integral Representations of Deviations of Linear Means of Fourier Series....Pages 43-79
Approximations by Fourier Sums in the Spaces c and L 1 ....Pages 81-208
Simultaneous Approximation of Functions and their Derivatives by Fourier Sums....Pages 209-254
Convergence Rate of Fourier Series and Best Approximations in the Spaces L p ....Pages 255-304
Best Approximations in the Spaces C and L ....Pages 305-345
Back Matter....Pages 347-366
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