Let be $\quad f(x)=\int_{0 }^{+\infty}cos\left(\frac{t^3}{3}+xt\right) d t$
Find the integral
$$F(x, y)=\int_{-\infty}^{+\infty} f(t+x) f(t+y) d t$$
I tried exploring f(x), took it in parts, got that it converges. F(x,y) is difficult to investigate, since the product of integrals is there, I don't know what to do with it.
You can noutice that $f(x)$ converges for all $x \in \mathbb{R}$
Improper integral that converges for all $x$ in $ \mathbb{R}$