Salomon Bochner studied at the University of Warsaw. His Ph.D. from the University of Berlin in 1921 was on orthogonal systems of complex analytic functions. It was supervised by Schmidt.
Bochner worked with Harald Bohr, Hardy and Littlewood in Copenhagen, Oxford and Cambridge respectively. Much of this work was on the zeta function.
Bochner lectured in Munich from 1924 to 1933 and developed major results in harmonic analysis. His work developed into the theory of distributions. Driven out of Germany in 1933 he accepted a position at Princeton where he remained until he retired. He worked at this time on summation of Fourier series and was considered as one of the greatest experts on Fourier analysis. Bochner worked jointly with von Neumann for a while. His major books include Harmonic Analysis and the Theory of Probability (1955). In the 1960s he worked on the history and philosophy of mathematics.