Zygmund's Book
Antoni Zygmond wrote a classic two-volume set of books entitled Trigonometric Series, which discusses many different aspects of these series, which we will not attempt to discuss here.The first edition was a single volume, published in 1935 (under the slightly different title "trigonometrical series"). The second edition of 1959 was greatly expanded, taking up two volumes, though it was later reprinted as a single volume paperback. The third edition of 2002 is similar to the second edition, with the addition of a preface by Robert A. Fefferman on more recent developments, in particular Carleson's theorem about pointwise convergence for continuous functions.
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