I read the following definition called Bump Algebra $B$:
Let $g(t)=e^{-t^2}$ be a normal Gaussian function. $$B := \left\{ f \in C(\mathbb{R}) : f = \sum_i a_i \, g \left( \frac{t-t_i}{s_i} \right) \right\}$$where the sum is countable, and $a_i\in \mathbb{R}$, $t_i\in \mathbb{R}$, $s_i>0$ and $\sum_i |a_i|<\infty$, and $C(\mathbb{R})$ denotes the set of continuous functions on $\mathbb{R}$.
How could I determine whether a function $h\in C(\mathbb{R})$ belongs to the Bump Algebra $B$.