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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| Main Authors: | , |
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| Format: | Artículo biblioteca |
| Language: | eng |
| Published: |
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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