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[函数] 存在通过所有点$(\frac1n,a_n)$的光滑函数吗?

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hbghlyj posted 2025-3-1 04:30 |Read mode
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$\{(\frac1n,a_n)\}_{n\ge1}$?

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original poster hbghlyj posted 2025-3-1 06:32
高人说:用bump function显然成立!

可惜没有下文

chat.stackexchange.com/transcript/message/67340980#67340980

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original poster hbghlyj posted 2025-3-1 07:29
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
chat.stackexchange.com/transcript/message/67341110#67341110

可惜没有下文

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