Elias M. Stein

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Elias Menachem Stein (born January 13, 1931) is a mathematician born in Belgium. Stein graduated from Stuyvesant High School in 1949 and received a Ph.D. from the University of Chicago in 1955. His advisor was Antoni Zygmund. Prizes awarded to Stein 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 2005, Stein was awarded the Stefan Bergman prize in recognition of his contributions in real, complex, and harmonic analysis.

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), Nikishin-Pisier-Stein factorization in operator theory, the Tomas-Stein restriction theorem in Fourier analysis, the Kunze-Stein phenomenon in convolution on nilpotent groups, the Cotlar-Stein lemma concerning the sum of almost orthogonal operators, and the Fefferman-Stein theory of the Hardy space <math>H^1</math> and the space <math>BMO</math> of functions of bounded mean oscillation.

He has written numerous books on harmonic analysis (see e.g. [1,2,3]), which have been so influential in that field that they are often cited as the standard references on the subject.

Stein is also noted for having an extraordinary number of graduate students (at least 43, according to the Mathematics Genealogy Project), including two Fields medalists Charles Fefferman and Terence Tao.

[edit] References

Stein, Elias (1970). Singular Integrals and Differentiability Properties of Functions. Princeton University Press. ISBN 0-691-08079-8.
Stein, Elias, Guido Weiss (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press. ISBN 0-691-08078-X.
Stein, Elias (1993). Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals. Princeton University Press. ISBN 0-691-03216-5.
Stein, Elias (2003). Fourier Analysis: An Introduction. Princeton University Press. ISBN 0-691-11384-X.
Stein, Elias (2003). Complex Analysis. Princeton University Press. ISBN 0-691-11385-8.
Stein, Elias (2005). Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Princeton University Press. ISBN 0-691-11386-6.