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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An elementary Tauberian theorem of nonlinear type


Authors: Harry Pollard and D. G. Saari
Journal: Proc. Amer. Math. Soc. 24 (1970), 593-594
MSC: Primary 26.40; Secondary 40.00
MathSciNet review: 0251168
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Abstract: We find a nonlinear condition on $ f \in {C^2}(0,\infty )$ which, when coupled with the assumption $ \lim \inf \vert f(t)\vert/t < \infty $, implies $ f \sim At$ and $ f' \to A$. $ A$ is some constant and $ t \to \infty $ or $ t \to 0 + $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0251168-2
Keywords: Tauberian Theorems, Asymptotic behavior of derivatives
Article copyright: © Copyright 1970 American Mathematical Society