Reference for "Approximation of identity" of a convolution

Question

I need a textbook reference for the "Approximation of identity" of a convolution:

http://en.wikipedia.org/wiki/Mollifier#Properties

I would appreciate any pointers. The wikipedia article refers to "every text on distribution theory" but I don't know where to start and the book by Hörmander does not seem to have this specific result.

Answer 1

Applied Analysis (by Hunter, Nachtergaele) is a first-year graduate text that covers Approximate Identities (among other things). Also you can get the chapters online from the author's websites.

https://www.math.ucdavis.edu/~hunter/book/pdfbook.html

Answer 2

Real Analysis by Stein and Shakarchi, section 3.2, is a good place to start. Alternately, Functional analysis by Rudin. Hörmander probably has it, but it'll be hard to find.