411 REFERENCE · Wikibooks
Differentiation and Integration in Several Real Variables/Test functions
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
We will consider two classes of test functions, namely bump functions and Schwartz functions.
Schwartz function Let . Then the Schwartz functions on are the set defined in the following way:
.
bump function Let . A bump function on is a function such that , the support of , is compact.
test functions are integrable Let or . Then .
{{proof|Suppose first . We know that on , attains a maximum by Weierstraß' theorem.