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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0251168-2
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 $\lim \inf |f(t)|/t < \infty$, implies $f \sim At$ and $fâ \to A$. $A$ is some constant and $t \to \infty$ or $t \to 0 +$.
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Keywords:
Tauberian Theorems,
Asymptotic behavior of derivatives
Article copyright:
© Copyright 1970
American Mathematical Society