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...
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| Autores principales: | , |
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| Formato: | Artículo |
| Lenguaje: | Inglés |
| Publicado: |
Springer Nature
2022
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| Materias: | |
| Acceso en línea: | https://repositorio.uca.edu.ar/handle/123456789/15167 |
| Aporte de: |
| Sumario: | 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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