Converse Sampling and Interpolation

Higgins, John R.

doi:10.1007/bf03549591

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Cited by 10 publications

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“…Recently, in [8] is obtained another possible converse with different choices of hypotheses. In the next section we give the preliminaries needed for the extension of this theorem to the Banach space setting.…”

Section: Introductionmentioning

confidence: 99%

Sampling basis in reproducing kernel Banach spaces

Centeno,

Medina

2018

Preprint

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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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Section: Introductionmentioning

confidence: 99%