does this equivalence show the conjugate symmetry property on a space of functions on same domain? Is this correct?
$$\int_{-\infty}^{+\infty} e^{-x^2} f^*(x)g(x) \, dx = \left(\int_{-\infty}^{+\infty} e^{-x^2} g^*(x)f(x) \, dx \right)^*$$
I am trying to show this is an inner product
can I take the *inside the integral on the RHS and for it to be equivalent to the left side once it is applied to $f$ and $g$.