Elias M. Stein

"Elias Stein" redirects here. For the Dutch chess player, see Elias Stein (chess player).

Elias M. Stein
Born	January 13, 1931 (1931-01-13) Antwerp, Belgium
Nationality	American
Fields	Mathematics
Institutions	Princeton University
Alma mater	University of Chicago
Doctoral advisor	Antoni Zygmund
Doctoral students	Charles Fefferman Christopher Sogge Robert Strichartz Terence Tao Gregg Zuckerman Steven G. Krantz
Notable awards	Rolf Schock Prize Wolf Prize

Elias Menachem Stein (born January 13, 1931) 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.

Biography

Stein was born to Elkan Stein and Chana Goldman, Ashkenazi Jews 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 H¹ and the space BMO 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 medalists, 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.

See also

• Stein–Strömberg theorem

Bibliography

• Stein, Elias (1970). Singular Integrals and Differentiability Properties of Functions. Princeton University Press. ISBN 0691080798. 
• Stein, Elias; Weiss, Guido (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press. ISBN 069108078X. 
• Stein, Elias (1971). Analytic Continuation of Group Representations. Princeton University Press. ISBN 0300014287. 
• Stein, Elias (1993). Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals. Princeton University Press. ISBN 0691032165. 
• Stein, Elias; Shakarchi, R. (2003). Fourier Analysis: An Introduction. Princeton University Press. ISBN 069111384X. 
• Stein, Elias; Shakarchi, R. (2003). Complex Analysis. Princeton University Press. ISBN 0691113858. 
• Stein, Elias; Shakarchi, R. (2005). Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Princeton University Press. ISBN 0691113866. 
• Stein, Elias; Shakarchi, R. (2011). Functional Analysis: An Introduction to Further Topics in Analysis. Princeton University Press. ISBN 0691113874. 

References

• This article incorporates material from Elias Stein on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

External links

• Elias M. Stein at the Mathematics Genealogy Project.
• Citation for Elias Stein for the 2002 Steele prize for lifetime achievement
• Elias Stein Curriculum Vitae

Academic offices
Preceded by Albert W. Tucker	Dod Professor of Mathematics at Princeton University 1975–present	Succeeded by incumbent