Concrete Example
Consider the function of the variable ℝn defined by
It is easily seen that this function is infinitely differentiable, non analytic with vanishing derivative for |x| = 1. Divide this function by its integral over the whole space to get a function of integral one, which can be used as mollifier as described above: it is also easy to see that defines a positive and symmetric mollifier.
Read more about this topic: Mollifier
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