Monday, 10 April 2017

real analysis - Approximation of continuous functions by a functions with vanishing second derivative

Denote by Cn[,+] the class of functions which: have finite limits at ±; and are differentiable n times on the line, with all these derivatives bounded. Denote by C30 the subclass of C3[,+] which have zero second derivative on R. Endow Cn[,+] with the supremum norm (so that, in particular, C30 inherits this norm).



My question is: is C30 dense in C3[,+] ?




Many thanks for your help.

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