The title says it all - is it possible to extend Schwartz's theory of distributions to N variables? I've heard that it can be easily extended to two variables using Schwartz's Kernel Theorem (does anyone know a good reference that explains this stuff?). Does this theorem carry over to N variables? Also, how does the notion of distributional derivative generalize to N variables? Finally, a largely unrelated question: I've seen assertions that hyperfunctions are "infinite order distributions." What does that even mean? What is the order of a distribution, and how do hyperfunctions relate to distribution theory? Any help would be greatly appreciated. Thank You in Advance.