STEIN, ELIAS M. / Mathematics / Researchers

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Mathematics / STEIN, ELIAS M.


Albert Baldwin Dod Professor of Mathematics at Princeton University, Mathematics Department.

Research interests


Elias Stein has made fundamental contributions to different branches of analysis.

In harmonic analysis, his Interpolation Theorem is a ubiquitous tool. His result about the relation between the Fourier transform and curvature revealed a deep and unsuspected property and has far reaching consequences.

His work on Hardy spaces has transformed the subject. He has made important contributions to the representation theory of Lie groups as well. His work on several complex variables is equally striking. His explicit approximate solutions for the ¯? -problems made it possible to prove sharp regularity results for solutions in strongly pseudoconvex domains. In this connection he also obtained subelliptic estimates which sharpened and quantified Hörmander’s hypoellipticity theorem for second order operators.

Prizes and awards

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 2005, Stein was awarded the Stefan Bergman prize in recognition of his contributions in real, complex, and harmonic analysis.


He has written numerous books on harmonic analysis, 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, which he penned for his celebrated sequence of undergraduate courses on analysis at Princeton, is rapidly becoming standard in introductory graduate and advanced undergraduate courses.

E.M. Stein, G.A. Margulis and A. Nevo,
Analogues of Wiener’s ergodic theorems for semi-simple Lie groups, II, Duke Math Journal, 103, (2000), 233-259.

E.M. Stein,
Some geometrical concepts arising in harmonic analysis, GAFA, Special Volume-GAFA2000, 434-453.

E.M. Stein, S.Wainger,
Discrete nalogues in harmonic analysis II: fractional integration, Journal d’Analyse Math., Vol. 80, (2000), 335-355.

E.M. Stein, D.H. Phong & Jacob Sturm,
Multilinear level set operators, oscillatory integral operators, and Newton polyhedra, Math. Ann., Vol. 319, (2001), 573-596.

E.M. Stein, A. Nagel & F. Ricci,
Singular Integrals with Flag Kernels and Analysis on Quadratic CR Manifolds, Journal of Functional Analysis, Vol. 181, (2001), 29-118.

E.M. Stein, A. Nagel,
Differentiable Control Metrics and Scaled Bump Functions, J. Differential Geometry, 57, (2001), 465-492.

E.M. Stein, A. Nagel,
The b-Heat equation on pseudoconvex manifolds of finite type in C2, Math. Zeit, 238, (2001), 37-88.

E.M. Stein, S. Wainger,
Oscillatory integrals related to Carleson’s theorem, Math. Res. Lett., 8, (2001), no. 5-6, 789-800.

E.M. Stein, A. Magyar and S. Wainger,
Discrete analogues in harmonic analysis: Spherical averages, Annals of Math., 155, (2002), 189-208.

E.M. Stein, S.Wainger,
Two discrete fractional integral operators revisted, Jour. d’Analyse Math., (2002), 87, 451-479.

E.M. Stein, R. Shakarchi,
Princeton Lectures in Analysis I, “Fourier Analysis: An Introduction,”
Princeton University Press, ISBN 0-691-11384-X, (2003).

E.M. Stein, R. Shakarchi,
Princeton Lectures in Analysis II, “Complex Analysis,” Princeton University Press, ISBN 0-691-11385-8, (2003).

E.M. Stein, A. Nagel,
On the product theory of singular integrals, Revista Iberoamericana, 20, (2004), 531-561.

E.M. Stein, L. Lanzani,
Szeg¨o and Bergman Projections on non-smooth planar domains, Jour. of Geometric Analysis, Vol. 14, (2004), 63-86.

E.M. Stein, R. Shakarchi,
Princeton Lectures in Analysis III “Real Analysis: Measure theory, integration, and Hilbert spaces,” Princeton University Press, (2005), ISBN 0-691-11386-6.

E.M. Stein, L. Lanzani,
A note on the div curl inequalities, Math. Research Letters, 12, (2005), 57-61.

E.M. Stein, A. Nagel,
The ¯@b-complex on decoupled boundaries in Cn, Annals of Math., 164, (2006), 649-713.
E.M. Stein, P. Gressman,
Regularity of the Fourier transform on spaces of homogeneous distributions, Jour. d’Analyse Math., vol. C, (2006), 211-222.

E.M. Stein, A. Gulisashvili,
Asymptotic behavior of the distribution of the stock price in models with stochastic volality: The Hull-White model, Comptes Rendus Acad. Science Paris, 343, (2006), 519-523.

E.M. Stein, A. Magyar and S. Wainger,
Maximal Operators Associated to Discrete Subgroups of Nilpotent Lie Groups, Journal D’Analyse Math., vol. 101, (2007), 257-312.

E.M. Stein, A. Ionescu, A. Magyar, and S. Wainger,
Discrete Radon transforms and applications to ergodic theory, (to appear in Acta Math.) July 24, 2007

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