[blt]

If the author is reading: In the proof, at the end of Step 6, it's confusing that the "uv" term of the integration by parts is suddenly given a range from -∞ to ∞, as if we had previously assumed x ∈ ℝ. But elsewhere in the article, including the examples, we have higher-dimensional x's. I suggest to either 1) include the full multidimensional version from the paper, or 2) explicitly mention that this is the simple 1d case, the same result holds in ℝ^n, and refer to the paper.

[cshimmin]

In the multidimensional case of integration by parts, the limit of integration is understood to be the (d-1 dimensional) boundary _at infinity _, so writing +/-inf is a reasonable shorthand. In almost all cases, it’s used when the term uv can be assumed to be zero (or at least constant) at this boundary.