On the coincidence of the spectra of random elliptic operators

S. M. Kozlov   ; M. A. Shubin

Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 455-471

Résumé

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.

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