Geodesic
On the hypoellipticity of infinite-dimensional differential operators
Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 269-278

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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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     author = {N. N. Frolov},
     title = {On the hypoellipticity of infinite-dimensional differential operators},
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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/