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Multipliers for Entire Functions and an Interpolation Problem of Beurling

✍ Scribed by Joaquim Ortega-Cerdà; Kristian Seip

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 160 KB
Volume: 162
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3357

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✦ Synopsis

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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