Spectrum of Periodically Correlated Fields
Keywords:
Periodically correlated processes, Stochastic processes and fields, Harmonizable processes, Spectrum, Shift operator, LCA group, Fourier transformAbstract
The paper deals with Hilbert space valued fields over any locally compact Abelian group G, in particular over G = Zn xRm, which are periodically correlated (PC) with respect to a closed subgroup of G. PC fields can be regarded as multi-parameter extensions of PC processes. We study structure, covariance function, and an analogue of the spectrum for such fields. As an example a weakly PC field over Z2 is thoroughly examined.
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