Abstract
Let \({\mathcal {F}}f\) be an abolutely convergent Fourier transform on the real line. We extend the following result of K. Karlander to \({\mathbf {R}^{n}}\) for \(n \ge 1\): Any closed reflexive subspace \(\{ {\mathcal {F}}f \}\) of the space of continuous functions vanishing at infinity is of finite dimension.
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Communicated by Hans G. Feichtinger.
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Walther, B.G. A Note on Spaces of Absolutely Convergent Fourier Transforms. J Fourier Anal Appl 20, 1328–1337 (2014). https://doi.org/10.1007/s00041-014-9353-2
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DOI: https://doi.org/10.1007/s00041-014-9353-2