Differentiation and Integration in Several Real Variables/Test functions

We will consider two classes of test functions, namely bump functions and Schwartz functions.

{{proof|Suppose first $$u \in \mathcal S(\mathbb R^n)$$. We know that on $$\overline B_1(0)$$, $$|u(x)|$$ attains a maximum by Weierstraß' theorem.

{{BookCat}}