Linear Fourier and stochastic analysis

Abstract

To extend the traditional Fourier theory of stationary processes, some new boundedness notions, for processes and for random measures, are introduced. This leads, for these processes and measures, to Plancherel and Hausdorff-Young type formulae and to a decomposition theory via dilations and multiplications. Various applications of our methods are also presented. © 1990 Springer-Verlag.