Geodesic
On $L^2$-functions with bounded spectrum
Sbornik. Mathematics, Tome 203 (2012) no. 11, pp. 1647-1653

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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 $\varphi\colon \mathbb R^m\to \mathbb R^n$ 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. Bibliography: 5 titles.
Keywords: functions with bounded spectrum, superposition operators.
Mots-clés : Fourier transform 
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     author = {V. V. Lebedev},
     title = {On $L^2$-functions with bounded spectrum},
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     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_11_a6/}
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V. V. Lebedev. On $L^2$-functions with bounded spectrum. Sbornik. Mathematics, Tome 203 (2012) no. 11, pp. 1647-1653. http://geodesic.mathdoc.fr/item/SM_2012_203_11_a6/