Hello all,

I have been trying to show that:

$\displaystyle (\digamma D_{c}f)(\gamma)= (D_{\frac{1}{c}}\digamma f) (\gamma)$

I have done the following so far:

$\displaystyle (\digamma D_{c}f)(\gamma)= \int_{ -\infty}^{\infty}(D_{c}f)(x)e^{-2\pi ix\gamma}dx=\int_{-\infty}^{\infty}\frac{1}{\sqrt{c}}f(\frac{x}{c})e^ {-2\pi ix\gamma}dx$

Now if we put $\displaystyle y=\tfrac{x}{c}$ we get:

$\displaystyle \int_{-\infty}^{\infty}\frac{1}{\sqrt{c}}f(y)e^{-2\pi iyc\gamma}cdy=\sqrt{c}\int_{-\infty}^{\infty}f(y)e^{-2\pi iyc\gamma}dy$

How do I continue so that I end up with what I intented to show?

Thanks a million