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The function $f:V \to \hat{\mathbb{R}}$ is said to be positively homogeneous iff $f(\alpha v) = \alpha f(v)$ for every $\alpha \in \mathbb{R}_{++}$. Here $V$ is a real vector space and $\hat{\mathbb{R}...

For Euclidean space $\mathbb{R}^n$, it is a well-known fact that the Schwartz space $\mathcal{S}(\mathbb{R}^n)$ is a Montel space. Moreover, the space of tempered distributions $\mathcal{S}'(\mathbb{R}...