存在通过所有点$(\frac1n,a_n)$的光滑函数吗？

hbghlyj · Posted at 2025-3-1 04:30:01

实数列$\an_{n\ge1}$需满足何种条件方可存在$\mathbb R$上的光滑函数通过所有点$\{(\frac1n,a_n)\}_{n\ge1}$？

hbghlyj · Posted at 2025-3-1 06:32:10

高人说：用bump function显然成立！

可惜没有下文

hbghlyj · Posted at 2025-3-1 07:29:13

高人又说：不太显然！

higher differentiability is, on second thought, a less obvious question

if worse comes to worst, you can always nuke this problem with Whitney

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[函数] 存在通过所有点$(\frac1n,a_n)$的光滑函数吗？