The Zero-Removing Property in Hilbert Spaces of Entire Functions Arising in Sampling Theory

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• 作者：A. G. García ; M. A. Hernández-Medina
• 关键词：46E22 ; 42C15 ; 94A20 ; Analytic Kramer kernel ; Lagrange ; type interpolation series ; zero ; removing property
• 刊名：Results in Mathematics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：67
• 期：3-4
• 页码：471-494
• 全文大小：639 KB
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• 作者单位：A. G. García (1)
  M. A. Hernández-Medina (2)
  
  1. Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911, Leganés-Madrid, Spain
  2. Departamento de Matemática Aplicada, E.T.S.I.T., U.P.M, Avda. Complutense 30, 28040, Madrid, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-9012

文摘

In the topic of sampling in reproducing kernel Hilbert spaces, sampling in Paley–Wiener spaces is the paradigmatic example. A natural generalization of Paley–Wiener spaces is obtained by substituting the Fourier kernel with an analytic Hilbert-space-valued kernel K. Thus we obtain a reproducing kernel Hilbert space \({\mathcal{H}_{K}}\) of entire functions in which the Kramer property allows to prove a sampling theorem. A necessary and sufficient condition ensuring that this sampling formula can be written as a Lagrange-type interpolation series concerns the stability under removal of a finite number of zeros of the functions belonging to the space \({\mathcal{H}_{K}}\); this is the so-called zero-removing property. This work is devoted to the study of the zero-removing property in \({\mathcal{H}_{K}}\) spaces, regardless of the Kramer property, revealing its connections with other mathematical fields.