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I am currently reading On Uniqueness Properties of Solutions of Schrödinger Equations and a having trouble understanding a claim made on page 1819. Context from the paper: let $g\in C^\infty_0(\...

Let $ A $ be a non-trivial $ C^{*} $-algebra and $ n \in \mathbb{N} $. Setting $ \mathcal{D} \stackrel{\text{df}}{=} A^{n} \setminus \{ (0_{A},\ldots,0_{A}) \} $, we can define a function $ f: \...