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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A property of infinitely differentiable functions


Author: Ha Huy Bang
Journal: Proc. Amer. Math. Soc. 108 (1990), 73-76
MSC: Primary 26E10
MathSciNet review: 1024259
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Abstract: The existence of $ {\lim _{n \to \infty }}\vert\vert{f^{(n)}}\vert\vert _p^{1/n}$ for an arbitrary function $ f(x) \in {C^\infty }({\mathbf{R}})$ such that $ {f^{\left( n \right)}}(x) \in {L^p}({\mathbf{R}}),n = 0,1, \ldots (1 \leq p \leq \infty )$ and the concrete calculation of $ {\lim _{n \to \infty }}\vert\vert{f^{(n)}}\vert\vert _p^{1/n}$ are shown.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1024259-9
PII: S 0002-9939(1990)1024259-9
Article copyright: © Copyright 1990 American Mathematical Society