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Multipliers for entire functions and an interpolation problem of Beurling
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We characterize the interpolating sequences for the Bernstein space of entire functions of exponential type, in terms of a Beurling-type density condition and a Carleson-type separation condition. Our work extends a description previously given by Beurling in the case that the interpolating sequences are restricted to the real line. An essential role is played by a multiplier lemma, which permits us to link techniques from Hardy spaces with entire functions of exponential type. We finally present a characterization of the sampling sequences for the Bernstein space, also extending a density theorem of Beurling.
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ORTEGA CERDÀ, Joaquim and SEIP, Kristian. Multipliers for entire functions and an interpolation problem of Beurling. Journal of Functional Analysis. 1999. Vol. 162, num. 2, pags. 400-415. ISSN 0022-1236. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/164425