On the coincidence of the spectra of random elliptic operators

A random elliptic operator of positive order is considered, whose coefficients are realizations of a homogeneous random field on $\mathbf R^n$ given by a dynamical system satisfying an aperiodicity condition indicating the absence of nontrivial periods of the corresponding unitary group. For such an operator, the coincidence of its spectra in $L^2(\mathbf R^n)$ and in the Hilbert space of homogeneous random fields is proved.
Bibliography: 21 titles.