On infinite dimensional periodically correlated random fields: Spectrum and evolutionary spectra

Infinite dimensional periodically correlated (PC) random fields are studied in spectral domain. A spectral characterization is given and harmonizability is established. The covariance operator is characterized where it is observed that an infinite dimensional PC field is a two-dimensional Fourier transform of a spectral random measure. Also, an evolutionary spectral representation and a space-dependent spectral density are given.