Prove that the Fourier transformation of (H_{k}(x) phi(x)) is ((i t)^{k} exp left(-frac{1}{2} t^{2}ight)). Hint: Use induction

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Prove that the Fourier transformation of \(H_{k}(x) \phi(x)\) is \((i t)^{k} \exp \left(-\frac{1}{2} t^{2}ight)\). Hint: Use induction and integration by parts as in the partial proof of Theorem 7.1.

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