Spectrum of periodically correlated fields

Abstract: The paper deals with Hilbert space valued fields over any locally compact Abelian group G, in particular over G = Z^n x R^m, 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 Z^2 is thoroughly examined.