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- W4313159022 abstract "We denote N, R, C the sets of natural, real and complex numbers respectively. Let (λn), n ∈ N be an unbounded sequence of complex numbers. Costakis has proved the following result. There exists an entire function f with the following property: for every x, y ∈ R with 0 , every θ ∈(0,1) and every a ∈ C there is a subsequence of natural numbers (mn), n ∈ N such that, for every compact subset L ⊆ C , In the present paper we show that the constant function a cannot be replaced by any non-constant entire function G. This is so even if one demands the convergence in (*) only for a single radius r and a single positive number θ. This result is related with the problem of existence of common universal vectors for an uncountable family of sequences of translation operators." @default.
- W4313159022 created "2023-01-06" @default.
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- W4313159022 date "2022-01-01" @default.
- W4313159022 modified "2023-09-30" @default.
- W4313159022 title "Uniform Convergence of Translation Operators" @default.
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- W4313159022 doi "https://doi.org/10.4236/apm.2022.1212054" @default.
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