Geodesic
On a class of pseudodifferential operators with an infinite number of variables, and applications
Sbornik. Mathematics, Tome 15 (1971) no. 3, pp. 443-491 
P. M. Bleher; M. I. Vishik. On a class of pseudodifferential operators with an infinite number of variables, and applications. Sbornik. Mathematics, Tome 15 (1971) no. 3, pp. 443-491. http://geodesic.mathdoc.fr/item/SM_1971_15_3_a4/
@article{SM_1971_15_3_a4,
     author = {P. M. Bleher and M. I. Vishik},
     title = {On a~class of pseudodifferential operators with an infinite number of variables, and applications},
     journal = {Sbornik. Mathematics},
     pages = {443--491},
     year = {1971},
     volume = {15},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_15_3_a4/}
}
TY  - JOUR
AU  - P. M. Bleher
AU  - M. I. Vishik
TI  - On a class of pseudodifferential operators with an infinite number of variables, and applications
JO  - Sbornik. Mathematics
PY  - 1971
SP  - 443
EP  - 491
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1971_15_3_a4/
LA  - en
ID  - SM_1971_15_3_a4
ER  - 
%0 Journal Article
%A P. M. Bleher
%A M. I. Vishik
%T On a class of pseudodifferential operators with an infinite number of variables, and applications
%J Sbornik. Mathematics
%D 1971
%P 443-491
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1971_15_3_a4/
%G en
%F SM_1971_15_3_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

In this work there are investigated pseudodifferential operators of an infinite number of variables whose symbols, roughly speaking, are comparable with a fractional power of a fixed elliptic quadratic form. A composition formula for such operators is proved. Applications are made to the theory of elliptic and parabolic operators of higher orders. Figures: 2. Bibliography: 8 titles.

[1] M. I. Vishik, “Parametriks ellipticheskikh operatorov s beskonechnym chislom nezavisimykh peremennykh”, Uspekhi matem. nauk, XXVI:2(158) (1971), 155–174

[2] Yu. L. Daletskii, “Beskonechnomernye ellipticheskie operatory i svyazannye snimi parabolicheskie uravneniya”, Uspekhi matem. nauk, XXII:4(136) (1967), 3–54

[3] M. Ann Piech, “A fundamental solution of parabolic equation on Hilbert space”, J. Functional Analysis, 3:1 (1969), 85–114 | DOI | MR

[4] S. V. Fomin, “Metod preobrazovaniya Fure dlya uravnenii v funktsionalnykh proizvodnykh”, DAN SSSR, 181:4 (1968), 812–814 | Zbl

[5] L. Gross, “Potential theory in Hilbert space”, J. Functional Analysis, 1 (1967), 123–181 | DOI | MR | Zbl

[6] P. A. Minlos, “Obobschennye sluchainye protsessy i ikh prodolzhenie do mery”, Trudy Mosk. matem. ob-va, 8 (1959), 497–518 | MR

[7] Dzh. Dzh. Kon, L. Nirenberg, “Algebra psevdodifferentsialnykh operatorov”, Psevdodifferentsialnye operatory, Mir, Moskva, 1967, 9–62 | MR

[8] M. S. Agranovich, M. I. Vishik, “Ellipticheskie zadachi s parametrom i parabolicheskie zadachi obschego vida”, Uspekhi matem. nauk, XIX:3(117) (1964), 53–161 | MR | Zbl