I'd like to point out that several of the concepts mentioned here are explained on the nLab:

<a href="http://nlab.mathforge.org/nlab/show/distribution#multiplication_of_distributions_7">multiplication of distributions</a>, 

while several are missing and the parts on microlocal analysis and <a href="http://nlab.mathforge.org/nlab/show/hyperfunction#multiplication_15">hyperfunctions</a> could use some help .