Abstract
Letf be an entire function in\(\mathbb{C}^n ,n \geqslant 1,\Lambda \subset \mathbb{C}^n ,E \subset \mathbb{C}^n .\). For a broad class of distribution densities of the set Λ, a scale of sufficient conditions for the completeness of the system of functions {f(λ×z):λ∈Λ},z∈E, where\(\lambda xz = (\lambda _1 z_1 ,\lambda _2 z_2 ,...,\lambda _n z_n )\), in the spaceH(E) of holomorphic functions onE with respect to the topology of uniform convergence on compact subsets is given in terms of the mutual indicator of the functionf and the setE. These conditions are new already forn=1 even ifE is a disk.
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Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 603–616, October, 1999.
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Khabibullin, B.N. Completeness of systems of entire functions in spaces of holomorphic functions. Math Notes 66, 495–506 (1999). https://doi.org/10.1007/BF02679100
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DOI: https://doi.org/10.1007/BF02679100