Geodesic
On a uniqueness theorem
Izvestiya. Mathematics, Tome 6 (1972) no. 1, pp. 241-248 Cet article a éte moissonné depuis la source Math-Net.Ru

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With an arbitrary solution of an operator equation of infinite order, a series of elementary solutions is associated. It is shown that if all coefficients of this series are zero, then the solution of the equation is identically zero. 
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Yu. N. Frolov. On a uniqueness theorem. Izvestiya. Mathematics, Tome 6 (1972) no. 1, pp. 241-248. http://geodesic.mathdoc.fr/item/IM2_1972_6_1_a7/

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[4] Frolov Yu. N., “O reshenii uravneniya beskonechnogo poryadka v obobschennykh proizvodnykh”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, LIXV, 1961, 294–315