August 20, 1899–May 2, 1982
BY ANTHONY W. KNAPP
SALOMON BOCHNER WAS A mathematician whose research profoundly influenced the development of a wide area of analysis in the last three-quarters of the twentieth century. He contributed to the fields of almost periodic functions, classical Fourier analysis, complex analysis in one and several variables, differential geometry, Lie groups, probability, and history of science, among others.
He did not often write long papers. Instead he would typically distill the essence of one or more topics he was studying, begin a paper with a treatment not far removed from axiomatics, show in a few strokes how some new theorem followed by making additional assumptions, and conclude with how that theorem simultaneously unified and elucidated old results while producing new ones of considerable interest. Part of the power of his method was that he would weave together his different fields of interest, using each field to reinforce the others. The effect on the body of known mathematics was often to introduce a completely new point of view and inspire other mathematicians to follow new lines of investigation at which his work hinted.
His early work on almost periodic functions on the line illustrates this approach. Harald Bohr of Copenhagen,