# Antoni Zygmund

**Antoni Zygmund** (December 25, 1900 – May 30, 1992) was a Polish mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century.^{[1]}^{[2]}^{[3]}^{[4]}^{[5]} 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 | |

Died | May 30, 1992 | (aged 91)

Nationality | Polish |

Citizenship | Polish, American |

Alma mater | University of Warsaw (Ph.D., 1923) |

Known for | Singular integral operators |

Awards | Leroy P. Steele Prize (1979) National Medal of Science (1986) |

Scientific career | |

Fields | Mathematics |

Institutions | University of Chicago Stefan Batory University |

Doctoral advisor | Aleksander Rajchman Stefan Mazurkiewicz |

Doctoral students | Alberto Calderón Elias M. Stein Paul Cohen |

## BiographyEdit

Born in Warsaw, Zygmund obtained his Ph.D. from the University of Warsaw (1923) and was a professor at Stefan Batory University at Wilno from 1930 to 1939, when World War II broke out and Poland was occupied. In 1940 he managed to emigrate to the United States, where he became a professor at Mount Holyoke College in South Hadley, Massachusetts. In 1945–1947 he was a professor at the University of Pennsylvania, and from 1947, until his retirement, 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 of the Polish Academy of Learning (*PAU*), from 1959 of the Polish Academy of Sciences (*PAN*), and from 1961 of the National Academy of Sciences in the United States. In 1986 he received the National Medal of Science.

In 1935 Zygmund published in Polish the original edition of what has become, in its English translation, the two-volume *Trigonometric Series*. It was described by Robert A. Fefferman as "one of the most influential books in the history of mathematical analysis" and "an extraordinarily comprehensive and masterful presentation of a ... vast field".^{[6]} Jean-Pierre Kahane called the book "The Bible" of a harmonic analyst. The theory of trigonometric series had remained the largest component of Zygmund's mathematical investigations.^{[5]}

His work has had a pervasive influence in many fields of mathematics, mostly in mathematical analysis, and particularly in harmonic analysis. Among the most significant were the results obtained with Calderón on singular integral operators.^{[7]}^{[6]} George G. Lorentz called it Zygmund's crowning achievement, one that "stands somewhat apart from the rest of Zygmund's work".^{[5]}

Zygmund's students included Alberto Calderón, Paul Cohen, Nathan Fine, Józef Marcinkiewicz, Victor L. Shapiro, Guido Weiss, Elias M. Stein and Mischa Cotlar. He died in Chicago.

## Mathematical objects named after ZygmundEdit

## BooksEdit

- Trigonometric Series (Cambridge University Press 1959, 2002)
- 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 alsoEdit

## ReferencesEdit

- ^
^{a}^{b}Noble, Holcomb B. (1998-04-20). "Alberto Calderon, 77, Pioneer Of Mathematical Analysis".*The New York Times*. ISSN 0362-4331. Retrieved 2019-06-23. - ^
^{a}^{b}Writer, Mark S. Warnick, Tribune Staff. "ALBERTO CALDERON, MATH GENIUS".*chicagotribune.com*. Retrieved 2019-06-23. - ^
^{a}^{b}"Antoni Zygmund (1900-1992)".*www-history.mcs.st-and.ac.uk*. Retrieved 2019-06-23. - ^
^{a}^{b}"PROFESSOR ALBERTO CALDERON, 77, DIES".*Washington Post*. ISSN 0190-8286. Retrieved 2019-06-22. - ^
^{a}^{b}^{c}Lorentz, G. G. (1993). "Antoni Zygmund and His Work" (PDF).*Journal of Approximation Theory*.**75**: 1–7. - ^
^{a}^{b}The 2nd edition of Zygmund's*Trigonometric Series*(Cambridge University Press, 1959) consists of 2 separate volumes. The 3rd edition (Cambridge University Press, 2002, ISBN 0 521 89053 5) consists of the two volumes combined with a foreword by Robert A. Fefferman. The nine pages in Fefferman's foreword (biographic and other information concerning Zygmund) are not numbered. **^**Carbery, Tony (17 July 1992). "Obituary: Professor Antoni Zygmund".*The Independent*.

## Further readingEdit

- Kazimierz Kuratowski,
*A Half Century of Polish Mathematics: Remembrances and Reflections*, Oxford, Pergamon Press, 1980, ISBN 0-08-023046-6. - Gray, Jeremy (1970–1980). "Zygmund, Antoni".
*Dictionary of Scientific Biography*.**25**. New York: Charles Scribner's Sons. pp. 414–416. ISBN 978-0-684-10114-9.