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Function Spaces and Partial Differential EquationsVolume 1 - Classical Analysis$
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Ali Taheri

Print publication date: 2015

Print ISBN-13: 9780198733133

Published to Oxford Scholarship Online: September 2015

DOI: 10.1093/acprof:oso/9780198733133.001.0001

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Abel-Poisson and Fejér Means of Fourier Series

Abel-Poisson and Fejér Means of Fourier Series

Chapter:
(p.75) 3 Abel-Poisson and Fejér Means of Fourier Series
Source:
Function Spaces and Partial Differential Equations
Author(s):

Ali Taheri

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198733133.003.0003

This chapter presents a thorough discussion of Fourier analysis on the circle and various summability methods, including Cesaro-Fejer and Abel-Poisson. The chapter also introduces the Banach algebra L1 and discussing some related concepts.

Keywords:   Fourier series, summability methods, Tauberian theorems, convolution Banach algebras, approximation to identity, Dirichlet kernel, Fejer kernel, Riemann-Lebesgue lemma

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