A converse sampling theorem in reproducing kernel Banach spaces
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.
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| Language: | eng |
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Springer Nature
2022
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| Subjects: | 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, |
| Online Access: | https://repositorio.uca.edu.ar/handle/123456789/15167 |
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oai:ucacris:123456789-151672022-10-20T13:59:29Z A converse sampling theorem in reproducing kernel Banach spaces Centeno, Hernán D. Medina, Juan M. 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 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. 2022-10-06T13:55:41Z 2022-10-06T13:55:41Z 2022 Artículo 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 1530-6429 https://repositorio.uca.edu.ar/handle/123456789/15167 10.1007/s43670-022-00026-6 eng Acceso restringido http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer Nature Theory Signal Process and Data Analysis 20, No.8, 2022 |
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Argentina |
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AR |
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| tag |
biblioteca |
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America del Sur |
| libraryname |
Sistema de bibliotecas de la UCA |
| language |
eng |
| topic |
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 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 |
| spellingShingle |
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 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 Centeno, Hernán D. Medina, Juan M. A converse sampling theorem in reproducing kernel Banach spaces |
| description |
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. |
| format |
Artículo |
| topic_facet |
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 |
| author |
Centeno, Hernán D. Medina, Juan M. |
| author_facet |
Centeno, Hernán D. Medina, Juan M. |
| author_sort |
Centeno, Hernán D. |
| title |
A converse sampling theorem in reproducing kernel Banach spaces |
| title_short |
A converse sampling theorem in reproducing kernel Banach spaces |
| title_full |
A converse sampling theorem in reproducing kernel Banach spaces |
| title_fullStr |
A converse sampling theorem in reproducing kernel Banach spaces |
| title_full_unstemmed |
A converse sampling theorem in reproducing kernel Banach spaces |
| title_sort |
converse sampling theorem in reproducing kernel banach spaces |
| publisher |
Springer Nature |
| publishDate |
2022 |
| url |
https://repositorio.uca.edu.ar/handle/123456789/15167 |
| work_keys_str_mv |
AT centenohernand aconversesamplingtheoreminreproducingkernelbanachspaces AT medinajuanm aconversesamplingtheoreminreproducingkernelbanachspaces AT centenohernand conversesamplingtheoreminreproducingkernelbanachspaces AT medinajuanm conversesamplingtheoreminreproducingkernelbanachspaces |
| _version_ |
1756276676426203136 |