Multipliers for entire functions and an interpolation problem of Beurling

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 sequence...

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Detalles Bibliográficos
Autores: Ortega Cerdà, Joaquim, Seip, Kristian
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:1999
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/164425
Acceso en línea:https://hdl.handle.net/2445/164425
Access Level:acceso abierto
Palabra clave:Funcions de variables complexes
Funcions enteres
Functions of complex variables
Entire functions
Descripción
Sumario: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.