Geodesic
On the hypoellipticity of infinite-dimensional differential operators
Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 269-278 Cet article a éte moissonné depuis la source Math-Net.Ru

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An infinite-dimensional differential operator with constant coefficients is considered in the paper. A number of necessary conditions for the hypoellipticity of such an operator are proved. These conditions are also sufficient for the hypoellipticity of finite-dimensional differential operators. Bibliography: 10 titles. 
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N. N. Frolov. On the hypoellipticity of infinite-dimensional differential operators. Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 269-278. http://geodesic.mathdoc.fr/item/SM_1977_31_2_a9/

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

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[5] N. N. Frolov, O zadache Dirikhle dlya ellipticheskikh differentsialnykh uravnenii s beskonechnomernymi operatorami, Dissertatsiya, Voronezh, 1970

[6] N. N. Frolov, “O zadache Dirikhle dlya ellipticheskogo operatora v tsilindricheskoi oblasti gilbertova prostranstva”, Matem. sb., 92 (134) (1973), 430–445 | MR | Zbl

[7] L. Gross, “Potential theory on Hilbert Space”, J. funct. analysis, 1:1 (1967), 123–181 | DOI | MR | Zbl

[8] Yu. L. Daletskii, S. N. Paramonova, “Ob odnoi formule teorii gaussovykh mer k otsenke stokhasticheskikh integralov”, Teoriya veroyatn., 1974, no. 4, 844–848

[9] G. E. Shilov, Fan Dyk Tin, Integral, mera i proizvodnaya na lineinykh prostranstvakh, izd-vo «Nauka», Moskva, 1967 | MR

[10] G. E. Shilov, Matematicheskii analiz (vtoroi spetsialnyi kurs), izd-vo «Nauka», Moskva, 1965 | MR