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Conditions for the completeness of the spectral domain of a harmonizable process

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  • Averkamp, Roland

Abstract

We generalize a theorem of Köthe and Toeplitz on unconditional bases in Hilbert spaces to Hilbert space-valued measures. This leads to a necessary and sufficient condition for the completeness of the spectral domain of a weakly harmonizable process whose shift operator exists and is invertible. A process in this class has a complete spectral domain if and only if it is the image of a stationary process under a topological isomorphism.

Suggested Citation

  • Averkamp, Roland, 1997. "Conditions for the completeness of the spectral domain of a harmonizable process," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 1-9, December.
    • Handle: RePEc:eee:spapps:v:72:y:1997:i:1:p:1-9
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    References listed on IDEAS

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    1. Dehay, Dominique, 1994. "Spectral analysis of the covariance of the almost periodically correlated processes," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 315-330, April.
    2. Hurd, Harry L., 1991. "Correlation theory of almost periodically correlated processes," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 24-45, April.
    3. Hurd, H. L., 1989. "Representation of strongly harmonizable periodically correlated processes and their covariances," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 53-67, April.
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