We describe the complete interpolating sequences for the Paley-Wiener spaces in terms of Muckenhoupt's () condition. For , this description coincides with those given by Pavlov , Nikol'skii , and Minkin  of the unconditional bases of complex exponentials in . While the techniques of these authors are linked to the Hilbert space geometry of , our method of proof is based on turning the problem into one about boundedness of the Hilbert transform in certain weighted spaces of functions and sequences.
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Yurii I. Lyubarskii, Kristian Seip, Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's () condition. Rev. Mat. Iberoam. 13 (1997), no. 2, pp. 361–376DOI 10.4171/RMI/224