Literature cited
V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, andKha T'en Ngoan, “Averaging and G-convergence of elliptic differential operators,” Usp. Mat. Nauk,34, No. 5, 65–133 (1979).
L. A. Pastur, “Spectra of random operators,” Usp. Mat. Nauk,28, No. 1, 3–64 (1973).
M. A. Shubin, “Spectral theory and index of elliptic operators with almost periodic coefficients,” Usp. Mat. Nauk,34, No. 2, 95–135 (1979).
A. I. Gusev, “Density of states and other spectral invariants of elliptic operators with random coefficients,” Mat. Sb.,104, No. 2, 207–226 (1977).
B. V. Fedosov and M. A. Shubin, “Index of random elliptic operators,” Mat. Sb.,108, 108–140, 453–483 (1978).
S. M. Kozlov, “Multidimensional spectral asymptotics for elliptic operators,” Dokl. Akad. Nauk SSSR,268, No. 4, 789–793 (1983).
S. M. Kozlov, “Distribution of eigenvalues of elliptic operators in large domains,” Usp. Mat. Nauk,37, No. 5, 185–186 (1982).
T. Kato, Theory of Perturbations of Linear Operators, Springer (1966).
N. G. Meyers, “An LP-estimate for the gradient of a solution of a second order equation,” Ann. Scuola Sup. Norm. Pisa,17, No. 2, 189–207 (1963).
D. G. Aronson, “Bounds for the fundamental solutions of a parabolic equation,” Bull. Am. Math. Soc.,73, No. 8, 890–896 (1967).
A. Friedman, Partial Differential Equations of Parabolic Type [Russian translation], Mir, Moscow (1968).
S. M. Kozlov, “Asymptotics of fundamental solutions of second-order divergent differential equations,” Mat. Sb.,113, No. 2, 302–323 (1980).
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Translated from Matematicheskie Zametki, Vol. 43, No. 3, pp. 407–423, March, 1988.
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Kozlov, S.M. Spectral asymptotics of random operators. Mathematical Notes of the Academy of Sciences of the USSR 43, 234–243 (1988). https://doi.org/10.1007/BF01138848
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DOI: https://doi.org/10.1007/BF01138848