While reading the Notation of the paper titled Geometric Deep Learning Grids, Groups, Graphs, Geodesics, and Gauges, I came across the following notations.
$$ \Omega = \text{ Domain} \\ u = \text{Point on domain} \\ x(u) \in \mathcal{X}(\Omega, C) = \text{ Signal on the domain of the form } x : \Omega \rightarrow C $$
Mathematically, a signal is just a function.
But, every function may not be a signal. There may be some distinction between a mathematical function and a signal.
When can I call any mathematical function a signal? And what is $\mathcal{X}$ in the notation given?
