Trigonometric Series

Antoni Zygmund wrote a classic two-volume set of books entitled Trigonometric Series, which discusses many different aspects of trigonometric series. 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 almost everywhere pointwise convergence for square-integrable functions.^{[citation needed]}

Publication history[]

• Zygmund, Antoni (1935), Trigonometrical series., Monogr. Mat., 5, Warszawa, Lwow: Subwencji Fundusz Kultury Narodowej., Zbl 0011.01703
• Zygmund, Antoni (1952), Trigonometrical series, New York: Chelsea Publishing Co., MR 0076084
• Zygmund, Antoni (1955), Trigonometrical series, Dover Publications, New York, MR 0072976
• Zygmund, Antoni (1959), Trigonometric series Vols. I, II (2nd ed.), Cambridge University Press, MR 0107776
• Zygmund, Antoni (1968), Trigonometric series: Vols. I, II, Second edition, reprinted with corrections and some additions (2nd ed.), Cambridge University Press, MR 0236587
• Zygmund, Antoni (1977), Trigonometric series. Vol. I, II, Cambridge University Press, ISBN 978-0-521-07477-3, MR 0617944
• Zygmund, Antoni (1988), Trigonometric series. Vol. I, II, Cambridge Mathematical Library, Cambridge University Press, ISBN 978-0-521-35885-9, MR 0933759
• Zygmund, Antoni (2002), Fefferman, Robert A. (ed.), Trigonometric series. Vol. I, II, Cambridge Mathematical Library (3rd ed.), Cambridge University Press, ISBN 978-0-521-89053-3, MR 1963498

Reviews[]

• Kahane, Jean-Pierre (2004), "Book review: Trigonometric series, Vols. I, II", Bulletin of the American Mathematical Society, 41 (3): 377–390, doi:10.1090/s0273-0979-04-01013-4, ISSN 0002-9904
• Salem, Raphael (1960), "Book Review: Trigonometric series", Bulletin of the American Mathematical Society, 66 (1): 6–12, doi:10.1090/S0002-9904-1960-10362-X, ISSN 0002-9904, MR 1566029
• Tamarkin, J. D. (1936), "Zygmund on Trigonometric Series", Bull. Amer. Math. Soc., 42 (1): 11–13, doi:10.1090/s0002-9904-1936-06235-x