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Advances in AnalysisThe Legacy of Elias M. Stein$
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Charles Fefferman, Alexandru D. Ionescu, D.H. Phong, and Stephen Wainger

Print publication date: 2014

Print ISBN-13: 9780691159416

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159416.001.0001

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Selected Theorems by Eli Stein

Selected Theorems by Eli Stein

(p.1) Chapter One Selected Theorems by Eli Stein
Advances in Analysis

Charles Fefferman

, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger
Princeton University Press

This chapter is an overview of the scope and originality of Eli Stein's contributions to analysis. His work deals with representation theory, classical Fourier analysis, and partial differential equations. He was the first to appreciate the interplay among these subjects, and to perceive the fundamental insights in each field arising from that interplay. No one else really understands all three fields, hence the need for this chapter. However, deep understanding of three fields of mathematics is by no means sufficient to lead to Stein's main ideas. Rather, at crucial points, Stein has shown extraordinary originality, without which no amount of work or knowledge could have succeeded.

Keywords:   Eli Stein, representation theory, selected theorems, classical Fourier analysis, partial differential equations, mathematics

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