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

Roland Averkamp

Stochastic Processes and their Applications, 1997, vol. 72, issue 1, 1-9

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.

Keywords: Weakly; harmonizable; process; Bimeasure; Completeness; of; spectral; domain; Shift; operator (search for similar items in EconPapers)
Date: 1997
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