Sampling basis in reproducing kernel Banach spaces
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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