# Elias stone

Elias Stein at the workshop "Real Analysis, Harmonic Analysis and Applications" in Oberwolfach , 2008

Elias Menachem Stein (born January 13, 1931 in Antwerp , Belgium , † December 23, 2018 ) was a Belgian-American mathematician who dealt with analysis and was considered a leading mathematician in the field of harmonic analysis .

## biography

Stein and his family fled from the National Socialists to the USA. He attended Stuyvesant High School in New York City and studied from 1949 at the University of Chicago . In 1955 he received his doctorate there under Antoni Zygmund (Linear Operators on Spaces). ${\ displaystyle L_ {p}}$In 1956 he was Moore Instructor at the Massachusetts Institute of Technology (MIT), in 1958 as an assistant professor at the University of Chicago and from 1963 professor at Princeton University . He was later Albert Baldwin Dod Professor of Mathematics there. In 1962/63 he was at the Institute for Advanced Study .

In 1984 and 2002 he received the Leroy P. Steele Prize , in 1993 the Rolf Schock Prize and in 1999 the Wolf Prize . In 2002 he received the National Medal of Science . He was a Sloan Research and Guggenheim Fellow and was a member of the National Academy of Sciences , the American Academy of Arts and Sciences, and the American Mathematical Society . In 2005 he received the Stefan Bergman Prize . In 2001 he received the Princeton University Prize for Excellence in Teaching. He gave a plenary lecture at the ICM in 1986 in Berkeley (Problems in harmonic analysis related to oscillatory integrals and curvature) and in 1970 in Nice (Some problems in harmonic analysis suggested by symmetric spaces and semi-simple groups).

Stein worked primarily in harmonic analysis, in particular on the development of the Calderón- Zygmund theory. Many of his textbooks became standard works and are widely used in the United States.

In 1972 he and Charles Fefferman proved the duality of the BMO space introduced by Louis Nirenberg and Fritz John from functions to the real Hardy space . ${\ displaystyle H ^ {1} (\ mathbb {R} ^ {n})}$

His PhD students included Fields Medal Prize winners Terence Tao and Charles Fefferman, as well as Robert Strichartz , Gregg Zuckerman and Stephen Gelbart .

## Fonts

• Singular Integrals and Differentiability Properties of Functions. Princeton University Press, 1970.
• with Guido Weiss : Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, 1971.
• Analytic Continuation of Group Representations. Princeton University Press, 1973.
• Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press, 1993.
• Fourier Analysis: An Introduction. Princeton University Press, 2003.
• Complex Analysis. Princeton University Press, 2003.
• Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Princeton University Press, 2003.

## literature

• Charles Fefferman , AD Ionescu, DH Phong, S. Wainger (Eds.): Advances in Analysis: The legacy of Elias M. Stein. Princeton University Press, 2014.