Abstract
The following result is proved.
Theorem.Let λ n ,0<λ n ↑∞, be a sequence of positive numbers with finite density
and let a compact set K has the following property: it intersects the real axis along the interval [a, b], where a is the very left point of K, B is the very right point of K; furthermore, K intersects every vertical straight line Re z=α, a≤α≤b, along an interval. If
2)
then
where
.
This result generalizes the theorem of Kaz'min [3]. Three corollaries are also proved, which generalize the theorems ofBoas [1] andPólya [6]. In the theorems of Boas and Pólya, we haveF(n)=0, ∀n ε Z. In our case
.
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лЕОНтьЕВА, Н.А. О стРУктУРЕ цЕлОИ ФУН кцИИ, ОБРАЩАУЩЕИсь В НУль Н А жАДАННОИ пОслЕДОВАтЕльНОстИ тОЧЕк. Analysis Mathematica 22, 171–186 (1996). https://doi.org/10.1007/BF02205217
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DOI: https://doi.org/10.1007/BF02205217