Remembering Paul Malliavin

P h o to g ra p h s , u n le s s o th e rw is e n o te d , c o u rt e s y o f T h é rè s e M a ll ia v in . On June 3, 2010, Paul Malliavin died at the American Hospital in Paris. At the time of his death, he was four months short of his eighty-fifth birthday. Malliavin was a major mathematical figure throughout his career. He studied under Szolem Mandelbrojt, who had returned to France after World War II from the United States, where he had been on the faculty of what, at the time, was the Rice Institute. Both Malliavin and Jean-Pierre Kahane received their degrees under Mandelbrojt in 1954, and Yitzhak Katznelson received his from Mandelbrojt a couple of years later. Thus, in less than three years, Mandelbrojt produced three students who would go on to become major figures in mid-twentieth-century harmonic analysis. Malliavin’s own singular contribution to harmonic analysis is described here by Kahane. Like many other definitive solutions to mathematical problems, Malliavin’s solution to the spectral synthesis problem killed the field, with the ironic consequence that few young mathematicians even know the statement of the problem, much less the name of the person responsible for its solution. Not one to rest on his laurels, Malliavin soon turned his attention in new directions. His early work won him an invitation to visit Arne Beurling at the Institute for Advanced Study, where, as Kahane explains here, during a second visit, Malliavin and Beurling completely solved two fundamental problems in classical complex variable theory. After completing his project with Beurling,