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18.104
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Spring 2013
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\begin{center}\textbf{Homework 10}\end{center}

\begin{center}Due April 4th by the beginning of class.\end{center}

\textbf{Problem:} Calculate the Fourier transform of $1_{(-1,1)}$ (this is the function $\mathbb R \to \{0,1\}$ which is $1$ on $(-1,1)$ and $0$ elsewhere) and use this result to calculate the Fourier transform of $x^k\sin x$ where $k \in \{-1,0,1,\dots\}$.

\textit{Hint:} For the first part use \cite[(8.1.1)]{frjo}, and for the second get the $k=-1$ case from the Fourier inversion formula for distributions, and for the other values of $k$ use \cite[(8.3.8)]{frjo}.

\textbf{Solution:}


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