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Linear Fourier and stochastic analysis
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  • Published: June 1990

Linear Fourier and stochastic analysis

  • Christian Houdré1 nAff2 

Probability Theory and Related Fields volume 87, pages 167–188 (1990)Cite this article

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  • 15 Citations

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Summary

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.

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Author information

Author notes
  1. Christian Houdré

    Present address: Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

Authors and Affiliations

  1. Center for Computational Statistics and Probability, George Mason University, 22030-4444, Fairfax, VA, USA

    Christian Houdré

Authors
  1. Christian Houdré
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Houdré, C. Linear Fourier and stochastic analysis. Probab. Th. Rel. Fields 87, 167–188 (1990). https://doi.org/10.1007/BF01198428

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  • Received: 02 November 1989

  • Revised: 17 March 1990

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01198428

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Keywords

  • Fourier
  • Stochastic Process
  • Stationary Process
  • Probability Theory
  • Mathematical Biology
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