This article is cited in 1 paper

On differential operators of infinite order in spaces of type $S$

Ya. I. Zhitomirskii


Abstract: 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.

UDC: 517.43

MSC: 47F05, 35A05, 35Exx

Received: 14.02.1969

 English version: Mathematics of the USSR-Sbornik, 1969, 9:3, 379–388

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