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Blueprint: rudin depends on rudin_exp
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YaelDillies committed Oct 30, 2023
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Expand Up @@ -50,7 +50,7 @@ \chapter{Chang's lemma}
If the discrete Fourier transform of $f : G \longrightarrow \C$ has dissociated support and $p \ge 2$ is an integer, then $\norm{f}_p \le 2 * \sqrt{pe} \norm f_2$.
\end{lemma}
\begin{proof}
\uses{rudin_exp_ineq}
\uses{rudin_exp}
\leanok
It is enough to show that $\norm{\Re f}_p \le \sqrt{pe} \norm f_2$ as then
$$\norm{f}_p \le \norm{\Re f}_p + \norm{i \Im f}_p = \norm{\Re f}_p + \norm{\Re (-if)}_p \le 2 \sqrt{pe} \norm f_2$$
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