Antoni Zygmund

Antoni Zygmund (December 25, 1900 – May 30, 1992) was a Polish mathematician. His main area of interest was harmonic analysis, and he is considered one of the greatest analysts of the 20th century.[1][2][3][4] Zygmund was responsible for creating the Chicago school of mathematical analysis together with his doctoral student Alberto Calderón, for which he was awarded the National Medal of Science in 1986.[1][2][3][4]

Antoni Zygmund
Antoni Zygmund
Born(1900-12-25)December 25, 1900
DiedMay 30, 1992(1992-05-30) (aged 91)
Chicago, Illinois, United States
CitizenshipPolish, American
Alma materWarsaw University (Ph.D., 1923)
Known forSingular integral operators
AwardsLeroy P. Steele Prize (1979)
National Medal of Science (1986)
Scientific career
InstitutionsUniversity of Chicago
Stefan Batory University
Doctoral advisorAleksander Rajchman
Stefan Mazurkiewicz
Doctoral studentsAlberto Calderón
Elias M. Stein
Paul Cohen


Born in Warsaw, Zygmund obtained his Ph.D. from Warsaw University (1923) and became a professor at Stefan Batory University at Wilno (1930–39). In 1940, during the World War II occupation of Poland, he emigrated to the United States and became a professor at Mount Holyoke College in South Hadley. From 1945 until 1947 he was a professor at the University of Pennsylvania, and from 1947 at the University of Chicago.

He was a member of several scientific societies. From 1930 until 1952 he was a member of the Warsaw Scientific Society (TNW), from 1946 a member of the Polish Academy of Learning (PAU), from 1959 a member of the Polish Academy of Sciences (PAN), and from 1961 a member of the National Academy of Science in Washington, D.C.. In 1986 he received the National Medal of Science.

His main interest was harmonic analysis. He wrote in Polish what soon became, in its English translation, the standard text in analysis, the two-volume Trigonometric Series. His students included Alberto Calderón, Paul Cohen, Nathan Fine, Józef Marcinkiewicz, Victor L. Shapiro, Guido Weiss, Elias Stein and Misha Cotlar. He died in Chicago.

His work has had a pervasive influence in many fields of mathematics, particularly in mathematical analysis. Perhaps most important was his work with Calderón on singular integral operators.

Mathematical objects named after Zygmund


  • Trigonometric Series (Cambridge University Press 1959, Dover 1955)
  • Intégrales singulières (Springer-Verlag, 1971)
  • Trigonometric Interpolation (University of Chicago, 1950)
  • Measure and Integral: An Introduction to Real Analysis, With Richard L. Wheeden (Marcel Dekker, 1977)

See also


  • Kazimierz Kuratowski, A Half Century of Polish Mathematics: Remembrances and Reflections, Oxford, Pergamon Press, 1980, ISBN 0-08-023046-6.
  • Zygmund, A. (2002) [1935], Trigonometric series. Vol. I, II, Cambridge Mathematical Library (3rd ed.), Cambridge University Press, ISBN 978-0-521-89053-3, MR 1963498[5][6][7]
  1. Noble, Holcomb B. (1998-04-20). "Alberto Calderon, 77, Pioneer Of Mathematical Analysis". The New York Times. ISSN 0362-4331. Retrieved 2019-06-23.
  2. Writer, Mark S. Warnick, Tribune Staff. "ALBERTO CALDERON, MATH GENIUS". Retrieved 2019-06-23.
  3. "Antoni Zygmund (1900-1992)". Retrieved 2019-06-23.
  4. "PROFESSOR ALBERTO CALDERON, 77, DIES". Washington Post. ISSN 0190-8286. Retrieved 2019-06-22.
  5. Salem, Raphael (1960). "Review: Trigonometric Series by A. Zygmund, 2nd. ed., vols. I and II" (PDF). Bull. Amer. Math. Soc. 66 (1): 6–12. doi:10.1090/S0002-9904-1960-10362-X.
  6. The 2nd edition (Cambridge U. Press, 1959) consists of 2 separate volumes. The 3rd edition (Cambridge U. Press, 2002) consists of the two volumes combined with a foreword by Robert A. Fefferman.
  7. Tamarkin, J. D. (1936). "Review: Trigonometric Series by A. Zygmund, 1st edn" (PDF). Bull. Amer. Math. Soc. 42 (1): 11–13. doi:10.1090/s0002-9904-1936-06235-x. The first edition (vol. V of the series Monografje Matematyczne, 1935) consists of iv+320 pp. The third edition consists of foreword: xii; vol. I: xiv+383 pp.; vol. II: viii+364 pp.

Further reading

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