In my course material I have the following notation $$ \varphi \in \mathcal{C}^{\infty}_{\mathcal{C}}(Z) $$ where $Z⊂R^{n}$ is a bounded open set. I was wondering what does this notation mean? What is the set $\varphi$ belongs into? Please, help me :)
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$\begingroup$ Is it really written with calligraphic C at both places? $\endgroup$– md2perpeCommented Jan 6, 2021 at 23:07
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1 Answer
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$\mathcal{C}^{\infty}_{\mathcal{C}}(Z)$ is the set of infinitely differentiable functions defined on $Z$ with compact support, i.e. they are zero outside some compact set.
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$\begingroup$ I've never seen it with a calligraphic C in either place. It's normally written $C_c^\infty(Z)$. But styles can vary. $\endgroup$– md2perpeCommented Jan 6, 2021 at 22:23
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$\begingroup$ @md2perpe I hadn't either, I'm only following the convention used by machniik. $\endgroup$– DMcMorCommented Jan 6, 2021 at 22:25