Geodesic
The index of random elliptic operators. I
Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 671-699 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This work is devoted to the construction of a theory of random elliptic operators; formulas are given for calculating the index of such an operator in terms of characteristic classes and the symbol of the operator. Bibliography: 15 titles. 
@article{SM_1978_34_5_a6,
     author = {B. V. Fedosov and M. A. Shubin},
     title = {The index of random elliptic {operators.~I}},
     journal = {Sbornik. Mathematics},
     pages = {671--699},
     year = {1978},
     volume = {34},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1978_34_5_a6/}
}
TY  - JOUR
AU  - B. V. Fedosov
AU  - M. A. Shubin
TI  - The index of random elliptic operators. I
JO  - Sbornik. Mathematics
PY  - 1978
SP  - 671
EP  - 699
VL  - 34
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/SM_1978_34_5_a6/
LA  - en
ID  - SM_1978_34_5_a6
ER  - 
%0 Journal Article
%A B. V. Fedosov
%A M. A. Shubin
%T The index of random elliptic operators. I
%J Sbornik. Mathematics
%D 1978
%P 671-699
%V 34
%N 5
%U http://geodesic.mathdoc.fr/item/SM_1978_34_5_a6/
%G en
%F SM_1978_34_5_a6
B. V. Fedosov; M. A. Shubin. The index of random elliptic operators. I. Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 671-699. http://geodesic.mathdoc.fr/item/SM_1978_34_5_a6/

[1] N. I. Akhiezer, I. M. Glazman, Teoriya lineinykh operatorov v gilbertovom prostranstve, izd-vo “Nauka”, Moskva, 1966 | MR

[2] I. Ts. Gokhberg, M. G. Krein, Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, izd-vo “Nauka”, Moskva, 1965 | MR

[3] A. I. Gusev, “Plotnost sostoyanii i drugie spektralnye invarianty samosopryazhennykh ellipticheskikh operatorov so sluchainymi koeffitsientami”, Matem. sb., 104(146) (1977), 207–226 | MR | Zbl

[4] A. I. Gusev, M. A. Shubin, “Ellipticheskie operatory so sluchainymi koeffitsientami”, Letnyaya shkola po teorii sluchainykh operatorov, Kiev, 1976

[5] N. Danford, Dzh. Shvarts, Lineinye operatory, t. 1, IL, Moskva, 1962

[6] L. A. Pastur, “Spektry sluchainykh samosopryazhenykh operatorov”, Uspekhi matem. nauk, XXVIII:1(169) (1973), 3–64 | MR

[7] B. V. Fedosov, “Analiticheskie formuly indeksa ellipticheskikh operatorov”, Trudy Mosk. matem. ob-va, XXX (1974), 159–241 | MR

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

[9] M. A. Shubin, “Pochti-periodicheskie ellipticheskie operatory”, Trudy vsesoyuznoi konferentsii po uravneniyam v chastnykh proizvodnykh, posvyaschennoi 75-letiyu so dnya rozhdeniya I. G. Petrovskogo, Moskva, 1976

[10] M. F. Atiyah, “Elliptic operators, discrete groups and von Neumann algebras”, Astérisqu, 32–33 (1976), 43–72 | MR | Zbl

[11] L. A. Coburn, R. D. Moyer, I. M. Singer, “$C^*$-algebras of almost periodic pseudo-differential operators”, Acta Math., 130:3–4 (1973), 279–307 | DOI | MR | Zbl

[12] M. D. Donsker, S. R. S. Varadhan, “Asimptotics for the Wiener sausage”, Comm. Pure-Appl. Math., 28:4 (1975), 525–565 | DOI | MR | Zbl

[13] H. Kumano-go, “Remarks on pseudo-differential operators”, J. Math. Soc. Japan, 21 (1969), 413–439 | Zbl

[14] H. Kumano-go, “Algebras of pseudo-differential operators”, J. Fac. Sci. Univ. Tokyo, Sec. 1A, 17:1–2 (1970), 31–50 | MR | Zbl

[15] R. T. Seeley, “Complex powers of an elliptic operator”, Proc. Symp. in Pure Math., 10 (1967), 288–307 | MR | Zbl