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Multipliers for Entire Functions and an Interpolation Problem of Beurling

机译:整函数的乘数与贝林的插值问题

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摘要

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.
机译:我们以贝林型密度条件和卡尔森型分离条件为特征,描述了指数型整个函数的伯恩斯坦空间的插值序列。我们的工作扩展了以前在插补序列仅限于实线的情况下由贝林格(Beurling)给出的描述。乘数引理起着至关重要的作用,它使我们能够将Hardy空间中的技术与整个指数类型的函数联系起来。最后,我们对伯恩斯坦空间的采样序列进行了描述,并扩展了贝林的密度定理。

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