Probability Theory and Related Fields

, Volume 87, Issue 2, pp 167–188

Linear Fourier and stochastic analysis

  • Christian Houdré

DOI: 10.1007/BF01198428

Cite this article as:
Houdré, C. Probab. Th. Rel. Fields (1990) 87: 167. doi:10.1007/BF01198428


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.

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Christian Houdré
    • 1
  1. 1.Center for Computational Statistics and ProbabilityGeorge Mason UniversityFairfaxUSA
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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