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https://repositorio.uca.edu.ar/handle/123456789/15167
Título : | A converse sampling theorem in reproducing kernel Banach spaces | Autor : | Centeno, Hernán D. Medina, Juan M. |
Palabras clave : | BASE DE MUESTREO; MUESTREO NO UNIFORME; REPRODUCCIÓN DE ESPACIOS DE HILBERT DEL KERNEL; REPRODUCCIÓN DE ESPACIOS DE BANACH DEL KERNEL; XD -FOTOGRAMAS; XD -BASE DE RIESZ; TEOREMAS DE MUESTREO DE KRAMER; PRODUCTOS SEMI-INTERIORES; MATEMATICA | Fecha de publicación : | 2022 | Editorial : | Springer Nature | Cita : | Centeno, H., Medina, J.M. A converse sampling theorem in reproducing kernel Banach spaces [en línea].Theory Signal Process and Data Analysis.2022, 20 (8). https://doi.org/10.1007/s43670-022-00026-6. Disponible en: https://repositorio.uca.edu.ar/handle/123456789/15167 | Resumen : | Abstract: We present a converse Kramer type sampling theorem over semi-inner product reproducing kernel Banach spaces. Assuming that a sampling expansion holds for every f belonging to a semi-inner product reproducing kernel Banach space B for a xed sequence of interpolating functions {a −1 j Sj (t)}j and a subset of sampling points {tj}j , it results that such sequence must be a X∗ d -Riesz basis and a sampling basis for the space. Moreover, there exists an equivalent (in norm) reproducing kernel Banach space with a reproducing kernel Gsamp such that {a −1 j Gsamp(tj , .)}j and {a −1 j Sj (.)}j are biorthogonal. These results are a generalization of some known results over reproducing kernel Hilbert spaces. | URI : | https://repositorio.uca.edu.ar/handle/123456789/15167 | ISSN : | 1530-6429 | Disciplina: | INGENIERIA | DOI: | 10.1007/s43670-022-00026-6 | Derechos: | Acceso restringido |
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