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Book Review

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Book Information:

Author: Antoni Zygmund
Title: Trigonometric series, Vols. I, II
Additional book information: third edition, with a foreword by Robert Fefferman, Cambridge Mathematical Library, Cambridge University Press, 2002, (Vol. I) xiv + 383 pp., (Vol. II) viii + 364, ISBN 0-521-89053-5, $60.00

References [Enhancements On Off] (What's this?)

  • 1. Selected papers of Antoni Zygmund, volume 1, A. Hulanicki, P. Wojtaszczyk and W. Zelazko, eds., 1989, Kluwer. MR 93a:01070a
  • 2. Collected papers of G.H. Hardy, volumes 3 and 6, 1969, 1974, Oxford, Clarendon Press. MR 41:24, MR 58:16073
  • 3. Seminars on thin sets in harmonic analysis, ed. Lindahl, L., and Poulsen, F., 1970, Institut Mittag-Leffler, Djursholm, Sweden, Lecture Notes in Pure and Applied Mathematics, Vol. 2. Marcel Dekker, Inc., New York, 1971. MR 52:14800
  • 4. Fourier analysis and related topics, 2002, Banach Center Publications volume 56, Institute of Mathematics, Polish Academy of Sciences. MR 2003k:42002
  • 5. C.C. GRAHAM and O.C. Mc GEHEE. Essays in commutative harmonic analysis. 1979, Springer-Verlag. MR 81d:43001
  • 6. H. HELSON. Harmonic analysis. 1983, Addison-Wesley. MR 85e:43001
  • 7. E. HEWITT and K.A. ROSS. Abstract harmonic analysis, I, II. 1963, 1970, Springer-Verlag. MR 28:158, MR 41:7378
  • 8. J.-P. KAHANE. Séries de Fourier absolûment convergentes. 1970, Springer-Verlag. MR 43:801
  • 9. J.-P. KAHANE and R. SALEM. Ensembles parfaits et séries trigonométriques. 1963 and 1994, Hermann. MR 28:3279, MR 96e:42001
  • 10. Y. KATZNELSON. An introduction to harmonic analysis. 1968, Wiley, New edition 2004, Cambridge University Press. MR 40:1734
  • 11. J.M. LOPEZ and R.A. ROSS. Sidon sets. 1975, Marcel Dekker. MR 55:13173
  • 12. M.B. MARCUS and G. PISIER. Random Fourier series with applications to harmonic analysis. 1981, Princeton University Press. MR 83b:60031
  • 13. Y. MEYER. Algebraic numbers and harmonic analysis. 1972, North-Holland. MR 58:5579
  • 14. W. RUDIN. Fourier analysis on groups. 1962, Interscience Publishers. MR 27:2808
  • 15. E.M. STEIN. Harmonic analysis, real-variable methods, orthogonality and oscillatory integrals. 1993, Princeton University Press. MR 95c:42002
  • 16. E.M. STEIN and R. SHAKARCHI. Fourier analysis, an introduction. 2003, Princeton University Press. MR 2004a:42001
  • 17. N.Y. ANTONOV. Convergence of Fourier series. East Journal on Approximations 2 (1996), 187-196. MR 97h:42005
  • 18. M. ASH and G. WANG. A survey of uniqueness questions in multiple trigonometric series. in Contemporary Mathematics 208 (1997), American Mathematical Society, 35-71. MR 99f:42019
  • 19. M. ASH and G. WANG. Some spherical uniqueness theorems for multiple trigonometric series. Annals of Mathematics 151 (2000), 1-33. MR 2001a:42009
  • 20. S.V. BOCHKAREV. Everywhere divergent Fourier-Walsh series. Doklady Mathematics 67 n$^{\circ}$3 (2003), 307-310.
  • 21. J. BOURGAIN. Sidon sets and Riesz products. Ann. Inst. Fourier 35 (1) (1985) 136-148. MR 86h:43009
  • 22. L. CARLESON. Convergence and growth of partial sums of Fourier series. Acta Mathematica 116 (1966), 135-157. MR 33:7774
  • 23. S. JAFFARD and Y. MEYER. Wavelet methods for pointwise regularity and local oscillations of functions. Memoir Amer. Math. Soc. 587 (1996). MR 97d:42005
  • 24. S.V. KONYAGIN. On everywhere divergence of trigonometric Fourier series. Sbornik Math. 191 (2000), 97-120. MR 2001e:42007
  • 25. H. LEBESGUE. Sur les intégrales singulières. Annales de la Faculté des Sciences de Toulouse (3) 1 (1909), 25-117.
  • 26. R. SALEM. Review: Trigonometric series (A. Zygmund), Bulletin American Mathematical Society 66 (1960), 6-12.

Review Information:

Reviewer: Jean-Pierre Kahane
Affiliation: Université Paris-Sud
Email: jean-pierre.kahane@math.u-psud.fr
Journal: Bull. Amer. Math. Soc. 41 (2004), 377-390
MSC (2000): Primary 42A16, 42A20, 42A24, 42A32, 42A33, 42A38, 42A50, 42A55, 42A63, 42B05, 42B10, 42B25
Published electronically: March 4, 2004
Review copyright: © Copyright 2004 American Mathematical Society
American Mathematical Society