In Chapter 0 of Iwaniec's Spectral Methods of Automorphic Forms Iwaneic uses the notation $C^{\infty}_{0}(\mathbb{R}^{+})$ without definition.
I assume that it's the set of infinitely differentiable functions from $\mathbb{R} \to \mathbb{R}$ with range a subset of the positive reals and which tend toward zero "sufficiently quickly," but I don't know whether my guess is right or what the precise definition of "sufficiently quickly" is in this context.
What does the subscript of $0$ refer to?