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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.

References [Enhancements On Off] (What's this?)

  • [1] A. N. Kolmogoroff, On inequalities between upper bounds of the successive derivatives of an arbitrary function on an infinite interval, Amer. Math. Soc. Transl. 4 (1949). MR 0031009 (11:86d)
  • [2] E. M. Stein, Functions of exponential type, Ann. of Math. (2)65 (1957), 582-592. MR 0085342 (19:23i)
  • [3] S. M. Nikolsky, Approximation of functions of several variables and imbedding theorems, "Nauka", Moscow, 1977. MR 506247 (81f:46046)

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