Examples
The function given by
is an example of a bump function in one dimension. It is clear from the construction that this function has compact support. The proof of smoothness follows along the same lines as for the related function discussed in the Non-analytic smooth function article. This function can be interpreted as the Gaussian function scaled to fit into the unit disc: the substitution corresponds to sending to
A simple example of a bump function in variables is obtained by taking the product of copies of the above bump function in one variable, so
Read more about this topic: Bump Function
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