There are some functions like $\sin x$, $\sin^2x$, $\sin x/x$, $\log(1+x)/(1+x)$ and other, that I have to distinguish which space they belong to. There are properties of vectors in different spaces to which the given functions are to satisfy to find out to which space they belong.
I think I am okay with Omega and Hilbert space, but I don't know how I can check if a vector belongs to Rigged Hilbert space based on the property of that space.
For reference, the property of a function belonging to Rigged Hilbert space is that the integral of the product of the complex conjugate of the function with any function belonging to Omega space must converge, the integral from $-\infty$ to $+\infty$.
With this reference, can anybody please explain me which of the spaces $\sin x$ belongs to and how. I would be very glad.