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On Boundedness of the l-ð\-Index of Entire Functions Represented by Series in a System of Functions
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On Boundedness of the l-ð\-Index of Entire Functions Represented by Series in a System of Functions
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Journal Article
On Boundedness of the l-ð\-Index of Entire Functions Represented by Series in a System of Functions
2024
Overview
Let f be an entire transcendental function and let (λn) be a sequence of positive numbers increasing to +∞. Suppose that the series AZ=∑n=1∞anfλnz is regularly convergent in ℂ, i.e., ð\"(r, A) := ∑n=1∞anMfrλn< + ∞ for all r ∈ [0,+ ∞). For a positive function l continuous on [0, + ∞), the function A is called a function of bounded l-ð\"-index if there exists N ∈ ℤ+ such that Mr,Ann!lnr≤maxMr,Akk!lkr:0≤k≤N for all n ∈ ℤ+ and all r ∈ [0,+ ∞). We study the properties of growth of the functions of bounded l- ð\"-index and formulate some unsolved problems.
Publisher
Springer Nature B.V
Subject
