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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?

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    $\begingroup$ I think $\chi$ is the set of all the signals over the domain. $\endgroup$ Sep 8, 2021 at 14:58

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