Geodesic
The index of random elliptic operators. II
Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 131-156 
B. V. Fedosov; M. A. Shubin. The index of random elliptic operators. II. Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 131-156. http://geodesic.mathdoc.fr/item/SM_1979_35_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For uniformly elliptic operators in $\mathbf R^n$ whose coefficients are smooth random functions which are homogeneous with respect to shifts in $\mathbf R^n$ the concept of an index is introduced and its properties are investigated. The index of a family of such operators is also defined. Formulas are established which express the index of an operator or a family of operators in terms of the principal symbol. Examples and special cases are considered. Bibliography: 9 titles.

[1] B. V. Fedosov, M. A. Shubin, “Indeks sluchainykh ellipticheskikh operatorov. I”, Matem. sb., 106(148) (1978), 108–140 | MR | Zbl

[2] B. V. Fedosov, “Teorema periodichnosti v algebre simvolov”, Matem. sb., 105(147) (1978), 431–464 | MR

[3] L. A. Coburn, R. D. Moyer, I. M. Singer, $C^*$-algebras of almost periodic pseudo-differential operators, Acta Math., 130, no. 3–4, 1973 | DOI | MR | Zbl

[4] Zh. Diksme, $C^*$-algebry i ikh predstavleniya, izd-vo “Nauka”, Moskva, 1974 | MR

[5] M. A. Shubin, “Differentsialnye i psevdodifferentsialnye operatory v prostranstvakh pochti-periodicheskikh funktsii”, Matem. sb., 95(137):4(12) (1974), 560–587 | MR | Zbl

[6] J. Dixmier, Les algèbres d'operateurs dans Tespace hilbertien (algèbres de von Neumann), Gauthier-Villars, Paris, 1969

[7] M. A. Shubin, “Psevdodifferentsialnye pochti-periodicheskie operatory i algebry fon Neimana”, Trudy Mosk. matem. ob-va, 35, 1976, 103–164 | Zbl

[8] M. A. Shubin, “Pochti-periodicheskie ellipticheskie operatory”, Vsesoyuznaya konferentsiya po uravneniyam s chastnymi proizvodnymi, posvyaschennaya 75-letiyu so dnya rozhdeniya I. G. Petrovskogo, Tezisy dokladov i soobschenii (Moskva, 1976), izd-vo MGU, Moskva, 1978, 245–248

[9] B. V. Fedosov, M. A. Shubin, “Ob indekse sluchainykh ellipticheskikh operatorov i ikh semeistv”, DAN SSSR, 236:4 (1977), 812–815 | MR | Zbl