Here's my problem:(adsbygoogle = window.adsbygoogle || []).push({});

I've got the Fourier transform of f(x) as Suppose that f is an integrable function. If [tex]\lambda \ne 0[/tex] is a real number and [tex] g(x) = f(\lambda x + y)[/tex] proove that

[tex]

G(k) = \frac{1}{\lambda} e^{ik/\lambda}F(\frac{k}{\lambda})

[/tex]

Where F and G are the Fourier transforms of f and g, respectively.

[tex]

F(K) = \frac{1}{\sqrt{2\pi}} \int\limits_{-\infty}^\infty f(x) e^{-ikx} dx

[/tex]

Likewise for g(x) I have

[tex]

G(K) = \frac{1}{\sqrt{2\pi}} \int\limits_{-\infty}^\infty g(x) e^{-ikx} dx

[/tex]

for F(K/lambda) I have

[tex]

F(K/\lambda) = \frac{1}{\sqrt{2\pi}} \int\limits_{-\infty}^\infty f(\lambda x + y) e^{-ik(\lambda x + y)/\lambda} d(\lambda x + y)

[/tex]

My guess is that the answer is relatively simple from here, but I'm not sure how to go about it. Does anyone understand this?

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# Homework Help: Problem with Fourier Transform

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