Harmonic Analysis and the Theory of Probability

The distinguished mathematician Salomon Bochner takes a probabilistic view in this classic text, emphasizing stochastic processes and the interchange of stimuli between probability and analysis. Non-probabilistic topics include Fourier series and integrals in many variables; the Bochner integral; and the transforms of Plancherel, Laplace, Poisson, and Mellin. This text's primary significance lies in the last two chapters, which offer a systematic presentation of Bochner's characteristic functional. A Fourier transform on a Euclidean-like space of infinitely many dimensions, the characteristic functional plays a role in stochastic processes similar to its relationship with numerical random variables. 1955 ed.