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Y. Okuyama, "Absolute Summability of Fourier Series and Orthogonal Series"

From the Preface

The purpose of these lecture notes is to study the absolute summa-

bility of Fourier series and orthogonal series. The absolute summabil-

ity is a generalization of the concept of the absolute convergence just

as the summability is an extension of the concept of the convergence.

The absolute convergence of Fourier series is closely related with

the variation and the modulus of continuity of functions. There are

several classical criteria for the absolute convergence of Fourier

series. We would like to show that these criteria can be systematically

proved from the point of view of the best approximation and that we can

offer some applications...

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