The zero-removing property in some Hilbert spaces of entire functions arising in sampling theory

García, A.G. and Hernandez Medina, Miguel Angel (2015). The zero-removing property in some Hilbert spaces of entire functions arising in sampling theory. "Results in Mathematics", v. 67 (n. 3); pp. 471-494. ISSN 1422-6383. https://doi.org/10.1007/s00025-014-0414-2.

Description

Title: The zero-removing property in some Hilbert spaces of entire functions arising in sampling theory
Author/s:
  • García, A.G.
  • Hernandez Medina, Miguel Angel
Item Type: Article
Título de Revista/Publicación: Results in Mathematics
Date: June 2015
ISSN: 1422-6383
Volume: 67
Subjects:
Freetext Keywords: Analytic Kramer kernel, Lagrange-type interpolation series, zero-removing property
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

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 HKHK 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 HKHK; this is the so-called zero-removing property. This work is devoted to the study of the zero-removing property in HKHK spaces, regardless of the Kramer property, revealing its connections with other mathematical fields.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2009-08345UnspecifiedUnspecifiedAproximación mediante fórmulas de muestreo en espacios invariantes por traslación: Aplicaciones

More information

Item ID: 41213
DC Identifier: http://oa.upm.es/41213/
OAI Identifier: oai:oa.upm.es:41213
DOI: 10.1007/s00025-014-0414-2
Official URL: http://link.springer.com/article/10.1007/s00025-014-0414-2
Deposited by: Memoria Investigacion
Deposited on: 29 Jun 2016 17:42
Last Modified: 29 Jun 2016 17:42
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