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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.

Answers