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Let $E=\mathbb{R}[X]$

We define $N:\, P \to \sum_{n=0}^{\infty} { |P^{(n)}(n)|}$ ($P^{(n)}$ being the $n$-th derivative) , it is not hard to prove that $N$ is a norm on $E$.

Help me to study the continuity of the linear form $f_m\colon\, P \to P_{[m]}$ ($P_{[m]}$ being the coefficient of $x^m$ in $P$) for some positive integer $m$.

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    actually for m=1 there is discontinuity2012-10-22

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