Elias Menachem Stein (January 13, 1931 – December 23, 2018) was an American mathematician who was a leading figure in the field of
harmonic analysis
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...
. He was the
Albert Baldwin Dod
Albert Baldwin Dod (March 24, 1805 – November 20, 1845) was an American Presbyterian theologian and professor of mathematics.
Early life
Dod was born on March 24, 1805, in Mendham, New Jersey. He was the son of Daniel Dod (1778–1823) and ...
Professor of Mathematics, Emeritus, at
Princeton University
Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
, where he was a faculty member from 1963 until his death in 2018.
Biography
Stein was born in Antwerp Belgium, to Elkan Stein and Chana Goldman,
Ashkenazi Jews
Ashkenazi Jews ( ; also known as Ashkenazic Jews or Ashkenazim) form a distinct subgroup of the Jewish diaspora, that emerged in the Holy Roman Empire around the end of the first millennium CE. They traditionally speak Yiddish, a language ...
from Belgium.
[University of St Andrews, Scotland - School of Mathematics and Statistics: "Elias Menachem Stein" by J.J. O'Connor and E F Robertson]
February 2010 After the
German invasion in 1940, the Stein family fled to the United States, first arriving in New York City.
He graduated from
Stuyvesant High School
Stuyvesant High School ( ) is a co-ed, State school, public, college-preparatory, Specialized high schools in New York City, specialized high school in Manhattan, New York City. The school, commonly called "Stuy" ( ) by its students, faculty, a ...
in 1949,
where he was classmates with future
Fields Medalist
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...
Paul Cohen
Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician, 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 awarded a F ...
, before moving on to the
University of Chicago
The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
for college. In 1955, Stein earned a Ph.D. from the
University of Chicago
The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
under the direction of
Antoni Zygmund
Antoni Zygmund (December 26, 1900 – May 30, 1992) was a Polish-American mathematician. He worked mostly in the area of mathematical analysis, including harmonic analysis, and he is considered one of the greatest analysts of the 20th century. ...
. He began teaching at
MIT
The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...
in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a full professor at Princeton.
Stein worked primarily in the field of
harmonic analysis
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...
, and made contributions in both extending and clarifying
Calderón–Zygmund theory. These include ''Stein interpolation'' (a variable-parameter version of
complex interpolation), the ''Stein maximal principle'' (showing that under many circumstances,
almost everywhere convergence
In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compared.
Definition
Suppose that X is a set and Y ...
is equivalent to the boundedness of
a
maximal function Maximal functions appear in many forms in harmonic analysis (an area of mathematics). One of the most important of these is the Hardy–Littlewood maximal function. They play an important role in understanding, for example, the differentiability pro ...
), ''
Stein complementary series representations'', ''Nikishin–Pisier–Stein factorization'' in operator theory, the ''Tomas–Stein restriction theorem'' in
Fourier analysis
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fo ...
, the ''Kunze–Stein phenomenon'' in
convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions f and g that produces a third function f*g, as the integral of the product of the two ...
on
semisimple group
In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group ''G'' over a perfect field is reductive if it has a representation that has a finite kernel and is a ...
s, the
Cotlar–Stein lemma concerning the sum of almost orthogonal operators, and the Fefferman–Stein theory of the
Hardy space
In complex analysis, the Hardy spaces (or Hardy classes) H^p are spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper . In real anal ...
and the space
of functions of bounded mean oscillation.
He wrote numerous books on harmonic analysis (see e.g.
,3,5, which are often cited as the standard references on the subject. His ''
Princeton Lectures in Analysis'' series
,7,8,9were penned for his sequence of undergraduate courses on analysis at Princeton. Stein was also noted as having trained a high number of graduate students. According to the
Mathematics Genealogy Project
The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. it contained information on 300,152 mathematical scientists who contributed to research-level mathematics. For a typical mathematicia ...
, Stein had at least 52 graduate students—including the
Fields medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...
ists
Charles Fefferman
Charles Louis Fefferman (born April 18, 1949) is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. He was awarded the Fields Medal in 1978 for his contribu ...
and
Terence Tao
Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the Co ...
—some of whom went on to shape modern Fourier analysis.
His honors included the
Steele Prize
The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories.
The prizes have b ...
(1984 and 2002), the
Schock Prize
The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm, Sweden, in 1993 and, since 2005, are awarded every three years. It is sometimes consider ...
in Mathematics (1993), the
Wolf Prize in Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. ...
(1999), and 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 science, behavior ...
(2001). In addition, he had fellowships to
National Science Foundation
The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...
,
Sloan Foundation
The Alfred P. Sloan Foundation is an American philanthropic nonprofit organization. It was established in 1934 by Alfred P. Sloan Jr., president and chief executive officer of General Motors.
The Sloan Foundation makes grants to support origin ...
,
Guggenheim Foundation, and
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
. Stein was elected as a member of the
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...
in 1982. In 2005, Stein was awarded the
Stefan Bergman
Stefan Bergman (5 May 1895 – 6 June 1977) was a Russian Poland, Poland-born American mathematician whose primary work was in complex analysis. He is known for the positive-definite kernel, kernel function he discovered in 1922 at Humboldt Univer ...
prize in recognition of his contributions in real, complex, and harmonic analysis. In 2012 he became a fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.
Personal life
In 1959, he married Elly Intrator.
They had two children, Karen Stein and
Jeremy C. Stein,
and grandchildren named Alison, Jason, and Carolyn. His son Jeremy is a professor of financial economics at Harvard, former adviser to
Tim Geithner and
Lawrence Summers
Lawrence Henry Summers (born November 30, 1954) is an American economist who served as United States Secretary of the Treasury from 1999 to 2001 and as the director of the National Economic Council from 2009 to 2010. He also served as presiden ...
, and served on the
Federal Reserve Board of Governors
The Board of Governors of the Federal Reserve System, commonly known as the Federal Reserve Board, is the main governing body of the Federal Reserve System. It is charged with overseeing the Federal Reserve Banks and with helping implement the mo ...
from 2012 to 2014. Elias Stein died of complications of
lymphoma
Lymphoma is a group of blood and lymph tumors that develop from lymphocytes (a type of white blood cell). The name typically refers to just the cancerous versions rather than all such tumours. Signs and symptoms may include enlarged lymph node ...
in 2018, aged 87.
Bibliography
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2011 reprint2010 reprint
2009 reprint
*
Notes
References
*
External links
*
*
Citation for Elias Stein for the 2002 Steele prize for lifetime achievementElias Stein Curriculum Vitae*
* – Extended video interview.
{{DEFAULTSORT:Stein, Elias M.
1931 births
2018 deaths
20th-century American mathematicians
21st-century American mathematicians
American people of Belgian-Jewish descent
Belgian emigrants to the United States
Belgian Jews
Fellows of the American Mathematical Society
Harmonic analysis
Jewish American scientists
Mathematicians from New York (state)
American mathematical analysts
Members of the United States National Academy of Sciences
National Medal of Science laureates
Princeton University faculty
Rolf Schock Prize laureates
Stuyvesant High School alumni
University of Chicago alumni
Wolf Prize in Mathematics laureates