Literature Cited
H. Muggli, “Differentialgleichungen unendlich hoher Ordnuug mit Constanten Koeffitienten,” Comment. Math. Helv.4, 151–179 (1938).
P. Van der Steen, On Differential Operators of Infinite Order, Diss., Delft (1968).
M. A. Kraplin, “On entire and meromorphic solutions of a class of difference equations,” Dokl. Akad. Nauk, SSSR,142, No. 5, 1011–1014 (1972).
Yu. F. Korobeynik and T. I. Demchenko, “On the solvability of a class of differential equations of infinite order,” Sib. Matem. Zh.8, No. 6, 1321–1338 (1967).
O. V. Epifanov, “Differential operators in spaces of entire functions of exponential type.” Thesis reports of the all soviet conference in the theory of functions of a complex variable, FTINT AN USSR, Khar'kov, 72–73 (1971).
O. V. Epifanov, “Normal resolvability of a differential operator in some spaces of entire functions of exponential type,” Sb. Matem. Analiz i ego prilozheniya, Izd-vo Rostov un-ta,4, 174–177 (1972).
Yu. F. Korobeynik and O. V. Epifanov, “Normal resolvability of a class of differential equations of infinite order,” Matem. Sb.84, (126), No. 3, 378–405 (1917).
Yu. F. Korobeynik, “Normal resolvable operators and differential equations of infinite order,” Lit. Matem. Sb.,11, No. 3, 569–595 (1971).
Zh. Sebasht'yan-i-Silva, “On some classes of locally convex spaces which are important in applications,” Matematika. Period. Sb. perev. in. statey1, No. 1, 60–77 (1957).
Yu. F. Korobeynik, O. V. Epifanov, “Estimates for derivatives in a weight space of entire functions,” Izv. AN. Arm. SSR,8, No. 2, 144–156 (1973).
M. G. Kreyn and I. Ts. Gokhberg, “New aspects of defect numbers, root numbers and indices of linear operators,” Uspekhi Matem. Nauk,12, No. 2 (74), 43–118 (1957).
R. Edwards, Functional Analysis [Russian translation], Mir, Moscow (1969).
V. P. Khavin, Spaces of Analytic Functions [in Russian], in: Matematicheskii analiz., Itogi nauki, Ser. “Matematika,” VINITI, Moscow (1967).
O. V. Eipfanov, “On the character of resolvability of differential equations of infinite order,” Sb. Matem. analiz. i ego Prilozheniya,1, Izd-vo Rostov un-ta, 72–83 (1969).
Yu. F. Korobeynik, “On the resolvability of a differential equation in the class of functions analytic in a convex region,” Matem. Sb.,75, (117), No. 2, 225–234 (1968).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 15, No. 2, pp. 318–331, March–April, 1974.
Rights and permissions
About this article
Cite this article
Epifanov, O.V. A differential operator of infinite order in the space of entire functions of exponential type. Sib Math J 15, 224–233 (1974). https://doi.org/10.1007/BF00968287
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968287