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Multiplication operators in spaces of entire functions of finite order and operators of convolution type. (English. Russian original) Zbl 0565.47018
Math. USSR, Sb. 48, 499-520 (1984); translation from Mat. Sb., Nov. Ser. 120(162), No. 4, 505-527 (1983).
This is a continuation of the author’s considerable and exhaustive work on convolution epimorphisms in complex analysis [see Dokl. Akad. Nauk. SSSR 217, 18-19 (1974; Zbl 0314.47023); Mat. Zametki 16, 415-422 (1974; Zbl 0331.47026); Mat. Zametki 15, 787-796 (1974; Zbl 0314.46050)]. In the present paper the author considers a continuous operation of multiplication by a particular function a(z), acting on certain spaces of entire functions of finite order and determines the condition for it to have a closed range. This is equivalent to determining the conditions under which the adjoint operator is a convolution epimorphism.
Reviewer: Ch.Sh.Sharma
MSC:
47B38 Linear operators on function spaces (general)
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
30D15 Special classes of entire functions of one complex variable and growth estimates
44A35 Convolution as an integral transform
43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
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