Spectrum of Periodically Correlated Fields

Dominique Dehay, Harry Hurd, Andrzej Makagon

Abstract

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.

Keywords

Periodically correlated processes; Stochastic processes and fields; Harmonizable processes; Spectrum; Shift operator; LCA group; Fourier transform

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