Abstract:
We consider the class PW(Rn) of functions in L2(Rn), whose Fourier transform has
bounded support. We obtain a description of continuous maps φ:Rm→Rn such that f∘φ∈PW(Rm) for every function f∈PW(Rn). Only injective affine maps φ have this property.
Bibliography: 5 titles.
Keywords:
Fourier transform, functions with bounded spectrum, superposition operators.
\Bibitem{Leb12}
\by V.~V.~Lebedev
\paper On $L^2$-functions with bounded spectrum
\jour Sb. Math.
\yr 2012
\vol 203
\issue 11
\pages 1647--1653
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Linking options:
https://www.mathnet.ru/eng/sm7906
https://doi.org/10.1070/SM2012v203n11ABEH004280
https://www.mathnet.ru/eng/sm/v203/i11/p121
This publication is cited in the following 3 articles:
Isao Ishikawa, “Bounded composition operators on functional quasi-Banach spaces and stability of dynamical systems”, Advances in Mathematics, 424 (2023), 109048
Masahiro Ikeda, Isao Ishikawa, Corbinian Schlosser, “Koopman and Perron–Frobenius operators on reproducing kernel Banach spaces”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 32:12 (2022)
Masahiro Ikeda, Isao Ishikawa, Yoshihiro Sawano, “Boundedness of composition operators on reproducing kernel Hilbert spaces with analytic positive definite functions”, Journal of Mathematical Analysis and Applications, 511:1 (2022), 126048
Citation in format AMSBIB
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