Abstract
The purpose of this paper is to show that the Rudin–Carleson interpolation theorem is a direct corollary of Fatou’s much older interpolation theorem (of 1906).
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Notes
Note that using the constructed sequence \(\{h_m\}\) one can easily derive the lemma on which the proofs of Doss [7] are based. Indeed, the functions \(h_m(z)[\lambda _E(z)]^m \in A\), being uniformly bounded on T by \(||f||_E\), obviously uniformly converge to f on E and converge to zero uniformly inside the complementary intervals of E (which implies the lemma used in [7]).
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The author wishes to thank the referees for the careful reading of the manuscript and useful suggestions.
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Communicated by Hans G. Feichtinger.
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Danielyan, A.A. Fatou’s Interpolation Theorem Implies the Rudin–Carleson Theorem. J Fourier Anal Appl 23, 656–659 (2017). https://doi.org/10.1007/s00041-016-9481-y
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DOI: https://doi.org/10.1007/s00041-016-9481-y