Elias M. Stein

Infobox_Scientist
name = Elias M. Stein


birth_date = Birth date and age|1931|1|13
birth_place = Belgium
residence =
nationality = USA
field = Mathematics
work_institution = Princeton University
alma_mater = University of Chicago
doctoral_advisor = Antoni Zygmund
doctoral_students = Charles Fefferman
Terence Tao
known_for =
author_abbreviation_bot =
author_abbreviation_zoo =
prizes = Rolf Schock Prize
Wolf Prize
religion =
footnotes =

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. 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.

Biography

Stein was born in Belgium. To escape Nazism, the Stein family fled to the United States, first arriving in New York. He graduated from Stuyvesant High School in 1949, [cite web |url=http://65.104.11.121/Math1948F.html |title=Stuyvesant Math Team, Fall 1948 |accessdate=2007-10-31] moving onto 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 the Massachusetts Institute of Technology 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 very useful 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 $H^1$ 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 have been so influential in that field that they are often cited as the standard references on the subject. His Princeton Lectures in Analysis series [5,6,7] , which he penned for his celebrated sequence of undergratuate courses on analysis at Princeton, is rapidly becoming standard in introductory graduate and advanced undergraduate courses.

Stein is also noted for having trained an unusually high number of successful graduate students (he has had at least 45 students, according to the Mathematics Genealogy Project), who have been very influential in shaping modern Fourier analysis. This includes two Fields medalists, Charles Fefferman and Terence Tao.

Stein has two children, Karen and Jeremy, as well as three grandchildren, Alison, Jason, and Carolyn.

ee also

* Stein-Strömberg theorem

References

*planetmath|id=9300|title=Elias Stein

Bibliography

*cite book | first=Elias | last=Stein | year=1970 | title=Singular Integrals and Differentiability Properties of Functions | publisher=Princeton University Press | isbn=0691080798
*cite book | first=Elias | last=Stein | coauthors=Weiss, Guido | year=1971 | title=Introduction to Fourier Analysis on Euclidean Spaces | publisher=Princeton University Press | isbn=069108078X
*cite book | first=Elias | last=Stein | year=1971| title=Analytic Continuation of Group Representations | publisher=Princeton University Press | isbn=0300014287
*cite book | first=Elias | last=Stein | year=1993 | title=Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals | publisher=Princeton University Press | isbn=0691032165
*cite book | first=Elias | last=Stein | year=2003 | title=Fourier Analysis: An Introduction | publisher=Princeton University Press | isbn=069111384X
*cite book | first=Elias | last=Stein | year=2003 | title=Complex Analysis | publisher=Princeton University Press | isbn=0691113858
*cite book | first=Elias | last=Stein | year=2005 | title=Real Analysis: Measure Theory, Integration, and Hilbert Spaces | publisher=Princeton University Press | isbn=0691113866

External links

*MathGenealogy |id=6454
* [http://www.ams.org/notices/200204/comm-steeleprz.pdf Citation for Elias Stein for the 2002 Steele prize for lifetime achievement]
* [http://www.math.princeton.edu/CV/SteinCV.pdf Elias Stein Curriculum Vitae]