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Does anybody know where can I find information about squared cosine/squared sine integral transform:

$$\int_{-\infty}^\infty f(x) \cos^2 (zx) dx$$

I want to see the list of such transforms over functions and/or know how to implement it in Mathematica.

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    by the double angle formula this transformation is equivalent to the usual cosine transform (if we had the standard integral over the infinite interval) – 2017-01-26
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    @tired I tried cosine transform and it gives 0 for function $\cos^2(x)$. I think it should give DiracDelta[1+x] – 2017-01-26
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    That is just the usual Fourier (cosine) transform in disguise. – 2017-01-26
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    @Jack D'Aurizio I cannot express it via cosine transform. You can? – 2017-01-26
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    @Anixx: just exploit $$\cos^2(xz) = \frac{1+\cos(2xz)}{2}$$ and a change of variable ($2z=\omega$). – 2017-01-26
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    @Jack D'Aurizio and what? How it will produce the first term? – 2017-01-26

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