 If the distribution "T" has compact support as well, then "f"∗"T" is a compactly supported function, and the Titchmarsh convolution theorem implies that

where "ch" denotes the convex hull and supp denotes the support.It is also possible to define the convolution of two distributions "S" and "T" on formula_85, provided one of them has compact support.Informally, in order to define "S"∗"T" where "T" has compact support, the idea is to extend the definition of the convolution ∗ to a linear operation on distributions so that the associativity formula

continues to hold for all test functions "formula_1".