Elias M. Stein
Encyclopedia
Elias Menachem Stein is a mathematician
and a leading figure in the field of harmonic analysis
. He is the Albert Baldwin Dod
Professor of Mathematics
at Princeton University
.
from Belgium
. After the German invasion in 1940
, the Stein family fled to the United States, first arriving in New York. He graduated from Stuyvesant High School
in 1949, moving on to the University of Chicago
for college. In 1955, Stein earned a Ph.D. from the University of Chicago
under the direction of Antoni Zygmund
. He began teaching in MIT in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a full professor at Princeton, the position he currently holds.
Stein has worked primarily in the field of harmonic analysis
, and has made major 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 is equivalent to the boundedness of
a maximal function
), Stein complementary series representations, Nikishin–Pisier–Stein factorization in operator theory, the Tomas–Stein restriction theorem in Fourier analysis, the Kunze–Stein phenomenon in convolution
on semisimple groups, the Cotlar–Stein lemma
concerning the sum of almost orthogonal operators, and the Fefferman–Stein theory of the Hardy space
and the space 
of functions of bounded mean oscillation.
He has written numerous books on harmonic analysis (see e.g. [1,2,4]), which are often cited as the standard references on the subject. His Princeton Lectures in Analysis series [5,6,7] were penned for his sequence of undergraduate courses on analysis at Princeton. Stein is also noted as having trained a high number of graduate students (he has had at least 45 students, according to the Mathematics Genealogy Project
), so shaping modern Fourier analysis. They include two Fields medal
ists, Charles Fefferman
and Terence Tao
.
Stein has two children, Karen and Jeremy (professor of financial economics at Harvard, formerly in Washington D.C. advising Tim Geithner and Laurence Summers), as well as three grandchildren.
His honors include the Steele Prize (1984 and 2002), the Schock Prize
in Mathematics (1993), the Wolf Prize in Mathematics
(1999), and the National Medal of Science
(2002). In addition, he has fellowships to National Science Foundation
, Sloan Foundation
, Guggenheim
, and National Academy of Sciences
. In 2005, Stein was awarded the Stefan Bergman
prize in recognition of his contributions in real, complex, and harmonic analysis.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and a leading figure in the field of harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
. He is the Albert Baldwin Dod
Albert Baldwin Dod
Albert Baldwin Dod was an American Presbyterian theologian and professor of mathematics. He was born in Mendham, New Jersey, and after a religious awakening while at college in Princeton, Dod became affiliated with the influential Princeton Theologians...
Professor of Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
.
Biography
Stein was born to Elkan Stein and Chana Goldman, Ashkenazi JewsAshkenazi Jews
Ashkenazi Jews, also known as Ashkenazic Jews or Ashkenazim , are the Jews descended from the medieval Jewish communities along the Rhine in Germany from Alsace in the south to the Rhineland in the north. Ashkenaz is the medieval Hebrew name for this region and thus for Germany...
from Belgium
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
. After the German invasion in 1940
Battle of Belgium
The Battle of Belgium or Belgian Campaign formed part of the greater Battle of France, an offensive campaign by Germany during the Second World War...
, the Stein family fled to the United States, first arriving in New York. He graduated from Stuyvesant High School
Stuyvesant High School
Stuyvesant High School , commonly referred to as Stuy , is a New York City public high school that specializes in mathematics and science. The school opened in 1904 on Manhattan's East Side and moved to a new building in Battery Park City in 1992. Stuyvesant is noted for its strong academic...
in 1949, moving on to the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
for college. In 1955, Stein earned a Ph.D. from the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
under the direction of Antoni Zygmund
Antoni Zygmund
Antoni Zygmund was a Polish-born American mathematician.-Life:Born in Warsaw, Zygmund obtained his PhD from Warsaw University and became a professor at Stefan Batory University at Wilno...
. He began teaching in MIT in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a full professor at Princeton, the position he currently holds.
Stein has worked primarily in the field of harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
, and has made major contributions in both extending and clarifying Calderón–Zygmund theory. These include Stein interpolation (a variable-parameter version of complex interpolation
Complex interpolation
In the field of mathematical analysis, an interpolation space is a space which lies "in between" two other spaces. The main applications are in Sobolev spaces, where spaces of functions that have a noninteger number of derivatives are interpolated from the spaces of functions with integer number of...
), the Stein maximal principle (showing that under many circumstances, almost everywhere convergence is equivalent to the boundedness of
a maximal function
Maximal function
Maximal functions appear in many forms in harmonic analysis . One of the most important of these is the Hardy–Littlewood maximal function. They play an important role in understanding, for example, the differentiability properties of functions, singular integrals and partial differential equations...
), Stein complementary series representations, Nikishin–Pisier–Stein factorization in operator theory, the Tomas–Stein restriction theorem in Fourier analysis, the Kunze–Stein phenomenon in convolution
Convolution
In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions. Convolution is similar to cross-correlation...
on semisimple groups, the Cotlar–Stein lemma
Cotlar–Stein lemma
In mathematics, in the field of functional analysis, the Cotlar–Stein almost orthogonality lemma is named after mathematicians Mischa Cotlarand Elias Stein...
concerning the sum of almost orthogonal operators, and the Fefferman–Stein theory of the Hardy space
Hardy space
In complex analysis, the Hardy spaces Hp are certain 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...
and the space of functions of bounded mean oscillation.He has written numerous books on harmonic analysis (see e.g. [1,2,4]), which are often cited as the standard references on the subject. His Princeton Lectures in Analysis series [5,6,7] were penned for his sequence of undergraduate courses on analysis at Princeton. Stein is also noted as having trained a high number of graduate students (he has had at least 45 students, according to the Mathematics Genealogy Project
Mathematics Genealogy Project
The Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...
), so shaping modern Fourier analysis. They include two Fields medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
ists, Charles Fefferman
Charles Fefferman
Charles Louis Fefferman is an American mathematician at Princeton University. His primary field of research is mathematical analysis....
and Terence Tao
Terence Tao
Terence Chi-Shen Tao FRS is an Australian mathematician working primarily on harmonic analysis, partial differential equations, combinatorics, analytic number theory and representation theory...
.
Stein has two children, Karen and Jeremy (professor of financial economics at Harvard, formerly in Washington D.C. advising Tim Geithner and Laurence Summers), as well as three grandchildren.
His honors include the Steele Prize (1984 and 2002), the Schock Prize
Schock prize
The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock . The prizes were first awarded in Stockholm, Sweden, in 1993 and have been awarded every two years since...
in Mathematics (1993), the Wolf Prize in Mathematics
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
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 sciences, biology, chemistry, engineering, mathematics and...
(2002). In addition, he has fellowships to National Science Foundation
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
, Sloan Foundation
Alfred P. Sloan Foundation
The Alfred P. Sloan Foundation is a philanthropic non-profit organization in the United States. It was established in 1934 by Alfred P. Sloan, Jr., then-President and Chief Executive Officer of General Motors.-Overview:...
, Guggenheim
Guggenheim Fellowship
Guggenheim Fellowships are American grants that have been awarded annually since 1925 by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation makes...
, and National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
. In 2005, Stein was awarded the Stefan Bergman
Stefan Bergman
Stefan Bergman was a Polish-born American mathematician whose primary work was in complex analysis. He is best known for the kernel function he discovered while at Berlin University in 1922. This function is known today as the Bergman kernel...
prize in recognition of his contributions in real, complex, and harmonic analysis.