抄録
We show that an integrable function on the real line with a nonnegative Fourier transform is square-integrable near the origin if and only if the transform belongs to the amalgam space comprised of functions that are locally integrable and globally square-integrable. We use this to give another proof that there are integrable functions on the real line that have nonnegative Fourier transforms and are square-integrable near the origin, but are not square-integrable on the whole real line. Our methods work on all locally compact abelian groups that are not compact. They also apply to other questions related to the one discussed above.
