Extensions and applications of a tauberian theorem due to valiron
1951 ◽
Vol 47
(1)
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pp. 22-37
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1. Introduction. In the course of an important memoir on integral functions of finite order†, G. Valiron discusses ‘fonctions orientées’, that is, functions with zeros an such that arg an tends to a limit as n → ∞. He obtains results that include the following two theorems, in which Vρ(x) denotes a function of the form , where α1, …, αν are positive integers, and n(r) has its usual significance in the theory of integral functions:.
2019 ◽
Vol 18
(09)
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pp. 1950167
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1959 ◽
Vol 249
(1256)
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Keyword(s):
2018 ◽
Vol 17
(08)
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pp. 1850145
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2014 ◽
Vol 51
(4)
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pp. 547-555
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2014 ◽
Vol 0
(0)
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2007 ◽
Vol 7
(3)
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pp. 239-254
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Keyword(s):
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2016 ◽