Analysis and applications: The mathematical work of Elias Stein

摘要

The purpose of this survey article is to give the general reader some idea of the scope and originality of Eli Stein’s contributions to analysis up to the year 1991. 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; therefore, no on else could have done the work I am about to describe. 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. Also, large parts of Steins’s work (e.g., the fundamental papers [27], [42], [48], [54], [65] on complex analysis in tube domains) don’t fit any simple one-paragraph description such as the one above.