Fourier series. A modern introduction. Vol. 2. 2nd ed. (English) Zbl 0599.42001

Graduate Texts in Mathematics, Vol. 85. New York - Heidelberg - Berlin: Springer-Verlag. XI, 369 p. DM 98.00; $ 40.90 (1982).
Preface: ”Apart from a number of minor corrections and changes, a substantial reformulation and updating of Chapters 14 and 15 has taken place. This reformulation and updating is a major and very welcome contribution from my friend and colleague, Dr. J. W. Sanders, to whom I express my sincere thanks. His efforts have product a much better result than I could have achieved on my own. Warm thanks are also due to Dr. Jo Ward, who checked some of the revised material. New Sections 16.9 and 16.10 have also been added. The bibliography has been expanded and brought up to date, though it is still not exhaustive.
In spite of these changes, the third paragraph in the preface to the revised edition of Volume 1 (1979; Zbl 0424.42001) is applicable here. What has been accomplished here is not a complete account of developments over the past 15 years; such an account would require many volumes. Even so, it may assist some readers who wish to appraise some of these developments.”


42-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42A20 Convergence and absolute convergence of Fourier and trigonometric series
42A24 Summability and absolute summability of Fourier and trigonometric series
40C05 Matrix methods for summability