Elias M. Stein

Elias Menachem Stein (January 13, 1931 – December 23, 2018) was an American mathematician who was a leading figure in the field of harmonic analysis. He was the Albert Baldwin Dod Professor of Mathematics, Emeritus, at Princeton University, where he was a faculty member from 1963 until his death in 2018.

Biography Stein was born in Antwerp, Belgium, 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 City. 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 at MIT in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a full professor at Princeton.

Stein worked primarily in the field of harmonic analysis, and 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 and the space of functions of bounded mean oscillation.

He wrote 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 was also noted as having trained a high number of graduate students. According to the Mathematics Genealogy Project, Stein had at least 52 graduate students—including the Fields Medal recipients Charles Fefferman and Terence Tao—some of whom went on to shape modern Fourier analysis.

His honors included 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 had fellowships to National Science Foundation, Sloan Foundation, Guggenheim Foundation, and National Academy of Sciences. Stein was elected as a member of the American Academy of Arts and Sciences in 1982. 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.

Personal life In 1959, he married Elly Intrator.