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18.104
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Spring 2013
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\begin{center}\textbf{Homework 7}\end{center}

\begin{center}Due March 7th by the beginning of class.\end{center}

\textbf{Problem:} Let $\lambda \in \mathbb C$ and let $u \in \mathscr{D}'(\mathbb R^n)$ be homogeneous of degree $\lambda$ in the sens of \cite[(4.2.12)]{frjo}. Show that $\partial^\alpha u$ is homogeneous of degree $\lambda - |\alpha|$ for any multiindex $\alpha$, and that
\[
\sum_{j=1}^n x_j \partial_j u = \lambda u.
\]

\textit{Hint:} Differentiate \cite[(4.2.12)]{frjo} with respect to $t$ and set $t=1$ (justifying carefully!).

\textbf{Solution:}


\begin{thebibliography}{00}
\bibitem[FrJo]{frjo} G. Friedlander and M. Joshi. The Theory of Distributions, second edition, Cambridge University Press, 1998.
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