World Library  
Flag as Inappropriate
Email this Article

Elias M. Stein

Article Id: WHEBN0000418073
Reproduction Date:

Title: Elias M. Stein  
Author: World Heritage Encyclopedia
Language: English
Subject: Antoni Zygmund, Wolf Prize in Mathematics, List of International Congresses of Mathematicians Plenary and Invited Speakers, Jeremy C. Stein, Steven G. Krantz
Collection: 1931 Births, 20Th-Century American Mathematicians, 21St-Century American Mathematicians, Alexander Von Humboldt Fellows, American Jews, American People of Belgian-Jewish Descent, Belgian Emigrants to the United States, Belgian Jews, Fellows of the American Mathematical Society, Guggenheim Fellows, Isi Highly Cited Researchers, Living People, Mathematical Analysts, Members of the United States National Academy of Sciences, National Medal of Science Laureates, Princeton University Faculty, Rolf Schock Prize Laureates, Stuyvesant High School Alumni, University of Chicago Alumni, Wolf Prize in Mathematics Laureates
Publisher: World Heritage Encyclopedia

Elias M. Stein

Elias M. Stein
Born (1931-01-13) January 13, 1931
Antwerp, Belgium
Nationality American
Fields Mathematics
Institutions Princeton University
Alma mater University of Chicago
Doctoral advisor Antoni Zygmund
Doctoral students Charles Fefferman
Christopher D. Sogge
Robert Strichartz
Terence Tao
Gregg Zuckerman
Steven G. Krantz
William E. Beckner
David Jerison
Notable awards Rolf Schock Prize in Mathematics (1993)
Wolf Prize in Mathematics (1999)
National Medal of Science (2001)
Leroy P. Steele Prize (2002)
Spouse Elly Intrator
Children Karen Stein
Jeremy C. Stein

Elias Menachem Stein (born January 13, 1931) is a mathematician active in the field of harmonic analysis. He is a professor emeritus of Mathematics at Princeton University.


  • Biography 1
  • Personal life 2
  • See also 3
  • Bibliography 4
  • Notes 5
  • References 6
  • External links 7


Stein was born to Elkan Stein and Chana Goldman, Ashkenazi Jews from Belgium.[1] After the German invasion in 1940, the Stein family fled to the United States, first arriving in New York.[1] He graduated from Stuyvesant High School in 1949,[1] where he was classmates with future Fields Medalist Paul Cohen,[2] before 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 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 H^1 and the space BMO of functions of bounded mean oscillation.

He has written numerous books on harmonic analysis (see e.g. [1,3,5]), which are often cited as the standard references on the subject. His Princeton Lectures in Analysis series [6,7,8,9] 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 51 students, according to the Mathematics Genealogy Project), so shaping modern Fourier analysis. They include two Fields medalists, Charles Fefferman and Terence Tao.

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 (2001). In addition, he has fellowships to National Science Foundation, Sloan Foundation, Guggenheim Foundation, 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. In 2012 he became a fellow of the American Mathematical Society.[3]

Personal life

In 1959, he married Elly Intrator,[1] a former Jewish refugee during World War II.[4] They had two children, Karen Stein and Jeremy C. Stein,[1] and grandchildren named Alison, Jason, and Carolyn. His son Jeremy is a former professor of financial economics at Harvard, former adviser to Tim Geithner and Lawrence Summers, and was appointed to the Federal Reserve Board of Governors by President Barack Obama in 2011.

See also


  • Stein, Elias (1970). Singular Integrals and Differentiability Properties of Functions.  
  • Stein, Elias (1970). Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Princeton University Press.  
  • Stein, Elias; Weiss, Guido (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press.  
  • Stein, Elias (1971). Analytic Continuation of Group Representations. Princeton University Press.  
  • Nagel, Alexander (1979). Lectures on Pseudo-differential Operators: Regularity Theorems and Applications to Non-elliptic Problems. Princeton University Press. [5] 
  • Stein, Elias (1993). Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals. Princeton University Press. [6] 
  • Stein, Elias; Shakarchi, R. (2003). Fourier Analysis: An Introduction. Princeton University Press.  
  • Stein, Elias; Shakarchi, R. (2003). Complex Analysis. Princeton University Press.  
  • Stein, Elias; Shakarchi, R. (2005). Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Princeton University Press.  
  • Stein, Elias; Shakarchi, R. (2011). Functional Analysis: An Introduction to Further Topics in Analysis. Princeton University Press.  


  1. ^ a b c d e University of St Andrews, Scotland - School of Mathematics and Statistics: "Elias Menachem Stein" by J.J. O'Connor and E F Robertson February 2010
  2. ^ "Stuyvesant High School Endowment Fund". Retrieved 2013-07-07. 
  3. ^ List of Fellows of the American Mathematical Society, retrieved 2013-08-05.
  4. ^ Center for Jewish History: "AHC interview with Elly Stein" 2012
  5. ^  
  6. ^ Ricci, Fulvio (1999). , by Elias Stein"Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals"Review: . Bull. Amer. Math. Soc. (N.S.) 36 (4): 505–521.  


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
Succeeded by
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.