On $L^2$ -functions with bounded spectrum

We consider the class $PW(\mathbb R^n)$ of functions in $L^2(\mathbb R^n)$, whose Fourier transform has bounded support. We obtain a description of continuous maps $φ: \mathbb R^m\rightarrow\mathbb R^n$ such that $f\circφ\in PW(\mathbb R^m)$ for every function $f\in PW(\mathbb R^n)$. Only injective affine maps $φ$ have this property.

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