Multipliers for Entire Functions and an Interpolation Problem of Beurling

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• 作者：Ortega-Cerdà ; Joaquim ; Seip ; Kristian
• 刊名：Journal of Functional Analysis
• 出版年：1999
• 出版时间：March 10, 1999
• 年：1999
• 卷：162
• 期：2
• 页码：400-415
• 全文大小：160 K

文摘

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.