Antoni Zygmund (December 25, 1900 – May 30, 1992) was a Polish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He worked mostly in the area of

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. Zygmund was responsible for creating the Chicago school of mathematical analysis together with his doctoral student

Alberto Calderón Alberto Pedro Calderón (September 14, 1920 – April 16, 1998) was an Argentinian mathematician. His name is associated with the University of Buenos Aires, but first and foremost with the University of Chicago, where Calderón and his mentor, t ...

, for which he was awarded the

National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social scienc ...

in 1986.

Biography

Born in

Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officia ...

, Zygmund obtained his Ph.D. from the

University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields o ...

(1923) and was a professor at

Stefan Batory University Vilnius University ( lt, Vilniaus universitetas) is a public research university, oldest in the Baltic states and in Northern Europe outside the United Kingdom (or 6th overall following foundations of Oxford, Cambridge, St. Andrews, Glasgow and ...

Wilno Vilnius ( , ; see also #Etymology and other names, other names) is the capital and List of cities in Lithuania#Cities, largest city of Lithuania, with a population of 592,389 (according to the state register) or 625,107 (according to the munic ...

from 1930 to 1939, when

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

broke out and Poland was

occupied ' (Norwegian: ') is a Norwegian political thriller TV series that premiered on TV2 on 5 October 2015. Based on an original idea by Jo Nesbø, the series is co-created with Karianne Lund and Erik Skjoldbjærg. Season 2 premiered on 10 October ...

. In 1940 he managed to emigrate to the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territori ...

, 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 The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

, and from 1947, until his retirement, at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

. He was a member of several scientific societies. From 1930 until 1952 he was a member of the

Warsaw Scientific Society Warsaw Scientific Society (Polish: ''Towarzystwo Naukowe Warszawskie''; TNW) is a Polish scientific society based in Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital ...

(''TNW''), from 1946 of the

Polish Academy of Learning The Polish Academy of Arts and Sciences or Polish Academy of Learning ( pl, Polska Akademia Umiejętności), headquartered in Kraków and founded in 1872, is one of two institutions in contemporary Poland having the nature of an academy of scie ...

(''PAU''), from 1959 of the

Polish Academy of Sciences The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society o ...

(''PAN''), and from 1961 of the National Academy of Sciences in the United States. In 1986 he received the

. In 1935 Zygmund published in Polish the original edition of what has become, in its English translation, the two-volume ''

Trigonometric Series In mathematics, a trigonometric series is a infinite series of the form : \frac+\displaystyle\sum_^(A_ \cos + B_ \sin), an infinite version of a trigonometric polynomial. It is called the Fourier series of the integrable function f if the term ...

''. 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".The 2nd edition of Zygmund's ''Trigonometric Series'' (

Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambridge University Pre ...

, 1959) consists of 2 separate volumes. The 3rd edition (Cambridge University Press, 2002, ) 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.

Jean-Pierre Kahane Jean-Pierre Kahane (11 December 1926 – 21 June 2017) was a French mathematician with contributions to harmonic analysis. Career Kahane attended the École normale supérieure and obtained the ''agrégation'' of mathematics in 1949. He then wor ...

called the book "The Bible" of a harmonic analyst. The theory of

trigonometric series In mathematics, a trigonometric series is a infinite series of the form : \frac+\displaystyle\sum_^(A_ \cos + B_ \sin), an infinite version of a trigonometric polynomial. It is called the Fourier series of the integrable function f if the term ...

had remained the largest component of Zygmund's mathematical investigations. 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 he obtained with Calderón on

singular integral operator In mathematics, singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular integral is an integral operator : T(f)(x) = \int K(x,y)f(y) \, dy, wh ...

George G. Lorentz George Gunter Lorentz (February 25, 1910 – January 1, 2006) was a Russian-American mathematician. Biography Lorentz was born in St. Petersburg. His father, Rudolf Fedorovich Lorentz, was a German railway engineer and his mother Milena Nikola ...

called it Zygmund's crowning achievement, one that "stands somewhat apart from the rest of Zygmund's work". Zygmund's students included

Paul Cohen Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician. He is best known for his proofs that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was award ...

, Nathan Fine, Józef Marcinkiewicz, Victor L. Shapiro,

Guido Weiss Guido Leopold Weiss (born 29 December 1928 in Trieste, died 25 December 2021 in St. Louis) was an American mathematician, working in analysis, especially Fourier analysis and harmonic analysis. Childhood Weiss was born in Trieste Italy int ...

Elias M. Stein Elias Menachem Stein (January 13, 1931 – December 23, 2018) was an American mathematician who was a leading figure in the field of harmonic analysis. He was the Albert Baldwin Dod Professor of Mathematics, Emeritus, at Princeton University, w ...

and Mischa Cotlar. He died in

Chicago (''City in a Garden''); I Will , image_map = , map_caption = Interactive Map of Chicago , coordinates = , coordinates_footnotes = , subdivision_type = Country , subdivision_name ...

Mathematical objects named after Zygmund

* Calderón–Zygmund lemma * Marcinkiewicz–Zygmund inequality *

Paley–Zygmund inequality In mathematics, the Paley–Zygmund inequality bounds the probability that a positive random variable is small, in terms of its first two moment (mathematics), moments. The inequality was proved by Raymond Paley and Antoni Zygmund. Theorem: If ''Z' ...

* Calderón–Zygmund kernel

Books

*Trigonometric Series (Cambridge University Press 1959, 2002) *Intégrales singulières (

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 ...

, 1971) *Trigonometric Interpolation (University of Chicago, 1950) *Measure and Integral: An Introduction to Real Analysis, With Richard L. Wheeden (

Marcel Dekker Marcel Dekker was a journal and encyclopedia publishing company with editorial boards found in New York City. Dekker encyclopedias are now published by CRC Press, part of the Taylor and Francis publishing group. History Initially a textbook pu ...

, 1977) *Analytic Functions, with

Stanislaw Saks Stanislav and variants may refer to: People * Stanislav (given name), a Slavic given name with many spelling variations (Stanislaus, Stanislas, Stanisław, etc.) Places * Stanislav, a coastal village in Kherson, Ukraine * Stanislaus County, C ...

(

Elsevier Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as '' The Lancet'', ''Cell'', the ScienceDirect collection of electronic journals, '' Trends'', ...

Science Ltd, 1971)

References

External links

*
Mount Holyoke biography
* {{DEFAULTSORT:Zygmund, Antoni 1900 births 1992 deaths People from Warsaw Governorate 20th-century Polish mathematicians Mathematical analysts National Medal of Science laureates Members of the Polish Academy of Learning University of Warsaw alumni Mount Holyoke College faculty University of Pennsylvania faculty University of Chicago faculty Academic staff of Vilnius University Polish emigrants to the United States Functional analysts Members of the Polish Academy of Sciences Members of the United States National Academy of Sciences

Biography

Mathematical objects named after Zygmund

Books

See also

References

Further reading

External links