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

[摘要] We generalize a theorem of Kothe 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. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-12-01

[关键词] weakly harmonizable process;bimeasure;completeness of spectral domain;shift operator