Please let me know the meaning of the notation $ C^q_c(0,1)$
what is the meaning of the notation $ C^q_c(0,1)$
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notation
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1seems "the space of functions on $(0,1)$ with $q$ continuous derivatives and with a compact support" – 2011-04-17
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5Notation questions would be easier to answer if the OP mentioned the book/article/whatever where s/he saw the entity in question. – 2011-04-17
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0I have seen this in an answer to this question at this link : http://mathoverflow.net/questions/61797/a-class-of-functions – 2011-04-17
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2Maybe you should have asked as a comment to Pietro's answer there, 'no? – 2011-04-17
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0@J.M. : I had some idea on it based on context (except for the subscript $c$. Now when i wanted to get clarified, i asked this question here as he doesn't seem to be online. – 2011-04-17
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4There's this thing called "patience" you know... – 2011-04-17
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0As user8268 points out the subscript $c$ means "with compact support". See also Pietro's second comment to his answer. – 2011-04-17
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0@Theo Buehler : I intended that $f$ has support in (0,1) but i wrote compact support in (0,1), but now i realize i had misconception. Kindly let me know the difference. Also if $f$ has support in (0,1) or [0,1], does it imply that $f$ has compact support ? – 2011-04-17
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0A compact subset of $(0,1)$ can't accumulate to either $0$ and $1$. So your function must vanish on a neighborhood of $0$ an $1$. But this clearly is incompatible with your first requirement in the MO question. Since your functions are defined on $(0,1)$ in the first place, adding "with support in $(0,1)$" is a bit redundant or I don't really know what your usage of support is. Usually it is the closure of the set of points where $f$ is non-zero. – 2011-04-17
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0@Theo Buehler : thanks for the comment. Please clear my doubt on this. I wanted $f$ to be defined on (0,1) and i assumed it could be zero everywhere. I realize my statement that "compact support in (0,1)" is not consistent and wrong. Please suggest how i should clarify this in the question. thank you – 2011-04-17
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0I would just cross out "with compact support in $(0,1)$" and probably I'd write $f:[0,1] \to \mathbb{R}$ since the requirement that $f$ be defined on all of $\mathbb{R}$ doesn't add anything to the content of the question. – 2011-04-17
1 Answers
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I recommend you to read Wikipedia article about Function Space.
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0Best suited as a comment. – 2018-01-17