Geodesic
On differential operators of infinite order in spaces of type $S$
Sbornik. Mathematics, Tome 9 (1969) no. 3, pp. 379-388 
Ya. I. Zhitomirskii. On differential operators of infinite order in spaces of type $S$. Sbornik. Mathematics, Tome 9 (1969) no. 3, pp. 379-388. http://geodesic.mathdoc.fr/item/SM_1969_9_3_a6/
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     title = {On~differential operators of infinite order in spaces of type~$S$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

I. M. Gel'fand and G. E. Shilov have investigated the action of differential operators of infinite order in spaces of type $S$. These differential operators were entire functions of a differential operator with constant coefficients, and on the basis of this they constructed an operational method in the problem of uniqueness of the solution of the Cauchy problem. The present work is devoted to the same problem for the case when the coefficients of the differential operator are variable and belong to the set of multiplicators of spaces of type $S$. Bibliography: 9 titles.

[1] G. E. Shilov, “Ob odnoi probleme kvazianalitichnosti”, DAN SSSR, 102:5 (1955), 893–895 | Zbl

[2] I. M. Gelfand, G. E. Shilov, “Preobrazovaniya Fure bystro rastuschikh funktsii i voprosy edinstvennosti resheniya zadachi Koshi”, Uspekhi matem. nauk, VIII:6(58) (1953), 3–55

[3] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii. Prostranstva osnovnykh i obobschennykh funktsii, vyp. 2, Fizmatgiz, M., 1958 | MR

[4] I. M. Gelfand, G. E. Shilov, “Ob odnom novom metode v teoremakh edinstvennosti resheniya zadachi Koshi dlya sistem lineinykh uravnenii v chastnykh proizvodnykh”, DAN SSSR, 102:6 (1955), 1065–1068

[5] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii. Nekotorye voprosy teorii differentsialnykh uravnenii, vyp. 3, Fizmatgiz, M., 1958 | MR

[6] Ya. I. Zhitomirskii, “Klassy edinstvennosti resheniya zadachi Koshi dlya lineinykh uravnenii s rastuschimi koeffitsientami”, Izv. AN SSSR, seriya matem., 31 (1967), 763–782 | Zbl

[7] Ya. I. Zhitomirskii, “Klassy edinstvennosti resheniya zadachi Koshi dlya lineinykh uravnenii s bystro rastuschimi koeffitsientami”, Izv. AN SSSR, seriya matem., 31 (1967), 1159–1178 | Zbl

[8] V. M. Borok, Ya. I. Zhitomirskii, “Zadacha Koshi dlya parabolicheskikh sistem, vyrozhdayuschikhsya na beskonechnosti”, Zapiski KhGU i Khark. matem. ob-va, 29:4 (1963), 5–15

[9] T. Yamanaka, “A refinement of the uniqueness bound of solutions of the Cauchy problem”, Funkcial. Ekvac., 11 (1968), 75–86 | MR | Zbl