On $L^2$ -functions with bounded spectrum

Details On $L^2$ -functions with bounded spectrum On $L^2$ -functions with bounded spectrum

2012-04-10

arxiv.org/abs/1204.2297v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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 $\varphi : \mathbb R^m\rightarrow\mathbb R^n$ such that
$f\circ\varphi\in PW(\mathbb R^m)$ for every function $f\in PW(\mathbb R^n)$.
Only injective affine maps $\varphi$ have this property.

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