This article is cited in 4 papers

On the coincidence of the spectra of random elliptic operators

S. M. Kozlov, M. A. Shubin


Abstract: 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.

UDC: 517.95

MSC: 47F05, 35R60, 35P05

Received: 04.10.1982

 English version: Mathematics of the USSR-Sbornik, 1985, 51:2, 455–471

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