Geodesic
On the coincidence of the spectra of random elliptic operators
Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 455-471

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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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     author = {S. M. Kozlov and M. A. Shubin},
     title = {On the coincidence of the spectra of random elliptic operators},
     journal = {Sbornik. Mathematics},
     pages = {455--471},
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     volume = {51},
     number = {2},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_51_2_a8/}
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S. M. Kozlov; M. A. Shubin. On the coincidence of the spectra of random elliptic operators. Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 455-471. http://geodesic.mathdoc.fr/item/SM_1985_51_2_a8/