Symmetry properties of higher spectral densities of stationary random processes (Q1100803)

The author deals with spectral densities \(f_{\nu}\) of the orders \(\nu =2,...,6\) of real-valued zero mean stationary time series. The base sets in \(R^{\nu -1}\) are described such that \(f_{\nu}(\lambda_ 1,...,\lambda_{\nu -1})\), \(\nu =2,...,6\), are completely defined by the values on these sets. It is proved that for \(\nu =3,...6\) there are \(2\nu\) ! of base sets with (\(\nu\)-1)-dimensional volumes \((2\pi)^{\nu - 1}/2\nu !\).