Literature Cited
G. E. Shilov, “On a problem of quasianalyticity,” Dokl. Akad. Nauk SSSR,102, No. 5, 893–896 (1955).
I. M. Gel'fand and G. E. Shilov, Generalized Functions, Vol. 2, Spaces of Fundamental and Generalized Functions, Academic Press, New York (1968).
V. A. Bogachev, “Differential operators of infinite order in weighted spaces of entire functions,” Author's Abstract of Candidate's Dissertation, Rostov-on-Don (1978).
H. Muggli, “Differentialgleichungen unendlich hoher Ordnung mit konstanten Koeffizienten,” Comment. Math. Helv.,11, 151–179 (1938).
A. O. Gel'fond, Calculus of Finite Differences [in Russian], Fizmatgiz, Moscow (1959).
B. Ya. Levin (B. J. Levin), Distribution of Zeros of Entire Functions, Amer. Math. Soc., Providence (1964).
V. A. Bogachev, “On a class of weighted spaces of entire functions,” Mat. Zametki,19, No. 2, 215–224 (1976).
Ya. M. Zhitomirskii, “On differential operators of infinite order in spaces of type S,” Math. Sb.,80, No. 3, 405–416 (1969).
I. M. Gel'fand and G. E. Shilov, Generalized Functions, Vol. 3, Theory of Differential Equations, Academic Press, New York (1967).
Yu. F. Korobeinik, “Differential equations of infinite order and infinite systems of differential equations,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 4, 881–922 (1970).
Yu. F. Korobeinik, “On the existence of solutions of equations of infinite order with a prescribed growth character,” Mat. Zametki,13, No. 5, 677–686 (1973).
N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Interscience, New York (1957).
O. V. Epifanov, “A differential operator of infinite order in spaces of entire functions of exponential type,” Sib. Mat. Zh.,15, No. 2, 318–331 (1974).
Additional information
Institute of Railroad Transportation Engineering, Rostov-on-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 22, No. 3, pp. 9–14, May–June, 1981.
Rights and permissions
About this article
Cite this article
Bogachev, V.A. Solvability of a differential equation of infinite order in certain spaces of type S. Sib Math J 22, 334–338 (1981). https://doi.org/10.1007/BF00969767
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00969767