What does $C^{2}_{0} [a,b]$ mean? I know that if a function is $C^{2}[a,b]$ its first and second derivatives exist and are continuous on the interval $[a,b]$. But I do not get what the $0$ in $C^{2}_{0}$ mean.
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It means "compactly supported". – Oct 17 '17 at 15:53
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@Jack But $[a,b]$ is compact already. And sometimes, as in $C_0(\mathbb R),$ it does not mean compact support. – zhw. Oct 17 '17 at 16:41
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You might be interested in this question as well: https://math.stackexchange.com/q/1561560/9464 – Oct 17 '17 at 17:30
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There are basically two possible meanings, which means that it should really be explicitly defined somewhere in the source you're referring to. The two possibilities are that the functions vanish on the boundary, and that their support is a compact subset of $(a,b)$. The latter is stronger than the former, and can be made more explicit by writing $C^k_c$.
Ian
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It usually means "compactly supported." It is sometimes also written $C_C^2[a,b]$.
davidlowryduda
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