A White Noise Theory of Infinite Dimensional Calculus

Sections 1-4 are based on those three lectures with somewhat more attention devoted to the space of generalized white noise functionals. What is described here are mostly survey articles, though some state-of-the-art results are added, while Section 5 involves a new approach to the study of Gaussian random fields. This topic is exactly what the author wished to propose at the colloquium. What is going to be presented here is, of course, far from a general theory however it is his hope that this attempt would be the very first step towards the study of Gaussian random fields using variational calculus. Contents White noise Generalized functionals Rotation group and harmonic analysis Applications to Physics Gaussian random fields. Keywords Statistic processes.