In Fourier analysis, a central theorem for the Fourier Transform states:
$$\mathcal F\{(f*g)(t)\}(\omega)=\mathcal F \{f(t)\}(\omega)\cdot \mathcal F\{g(t)\}(\omega)$$
In other words, convolution turns into multiplication.
In turn convolution is defined as $$(f*g)(t)=\int_{-\infty}^\infty f(\tau)g(t-\tau)d\tau$$
A correllation can be defined similarly:
$$corr(f,g) =\int_{-\infty}^\infty f(\tau)g(\tau-t)d\tau$$
How can we figure out which (if any) integral transform which has a similar rule for correllation as the Fourier Transform has for convolution?
Surely there is! It's called the cross correlation theorem for Fourer transform. There's also a similar theorem for Laplace transform (the theorem is stated in the table in the link given, just search for "cross correlation").