Thanks Tim.
No the paper didn't give any references. Which theorems are you referring to? I'd like to look them up. What do you mean by a "subsidiary integral in the middle of a much larger integration"?
I'm sorry to ask so many annoying questions.
I'm trying to understand a paper in which the authors use a number of test functions (are they the same as convergence factors) to make integrate unintegrable functions. Now here is my ignorant question: why is this acceptable? The product of the original function and the test function or...