Difference between revisions of "Aufgaben:Problem 15"
From Ferienserie MMP2
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$$ f \cdot \mu_{\partial B} : \mathcal D (\mathbb{R}^3) \rightarrow \mathbb{R}^3 $$ | $$ f \cdot \mu_{\partial B} : \mathcal D (\mathbb{R}^3) \rightarrow \mathbb{R}^3 $$ | ||
| − | $$ \phi \mapsto (f \cdot \mu_{\partial B})(\phi) = \int_{\partial B} $$ | + | $$ \phi \mapsto (f \cdot \mu_{\partial B})(\phi) = \int_{\partial B} f(x') \phi(x') dx' $$ |
Revision as of 16:25, 9 June 2015
Let \( f \) be a continuous real-valued function on \( \mathbb{R}^n \). Let \(B = B_1(0) \) denote the unit ball in \( \mathbb{R}^3 \) . We define
$$ 1_B= \begin{cases} 1 \space x \in B \\ 0\space x\notin B \end{cases} $$
and a linear map
$$ f \cdot \mu_{\partial B} : \mathcal D (\mathbb{R}^3) \rightarrow \mathbb{R}^3 $$ $$ \phi \mapsto (f \cdot \mu_{\partial B})(\phi) = \int_{\partial B} f(x') \phi(x') dx' $$
