Bump function

In mathematics, a bump function is a function f : Rⁿ → R on a Euclidean space Rⁿ which is both smooth (in the sense of having continuous derivatives of all orders) and compactly supported. These are also called test functions [φ]. The space of all bump functions on Rⁿ is denoted ${\displaystyle C_{0}^{\infty }(\mathbf {R} ^{n})}$ or ${\displaystyle C_{c}^{\infty }(\mathbf {R} ^{n})}$. The dual space of this space endowed with a suitable topology is the space of distributions.

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