Sampling basis in reproducing kernel Banach spaces

2018/07/06 by Hernán D. Centeno, Centeno, Hernán D., Juan Miguel Medina +2
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Banach space #Basis (linear algebra) #Computer science #Discrete mathematics #FOS: Mathematics #Functional Analysis (math.FA) #Functional analysis #Generalization #Geometry #Hilbert space #Interpolation space #Kernel (algebra) #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Pure mathematics #Reproducing kernel Hilbert space #Sampling (signal processing) #Sequence (biology) #Type (biology) #math.FA

paper · pdf · doi:10.48550/arxiv.1807.02218

published in arXiv (Cornell University) (Cornell University)

arxiv created 2018/07/06 · openalex publication_date 2018/07/06 · arxiv updated 2018/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present necessary and sufficient conditions to hold true a Kramer type sampling theorem over semi-inner product reproducing kernel Banach spaces. Under some sampling-type hypotheses over a sequence of functions on these Banach spaces it results necessary that such sequence must be a X_d-Riesz basis and a sampling basis for the space. These results are a generalization of some already known sampling theorems over reproducing kernel Hilbert spaces.

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