Irregular stable sampling and interpolation in functional normed spaces
DOI:
https://doi.org/10.5269/bspm.45497Abstract
We define the concepts of stable sampling set and stable interpolation set, uniqueness set and complete interpolation set for a normed space of functions. In addition we will show some relationships between these concepts. The main relationships arise when one wants to reduce an stable sampling set or to extend an stable interpolation set. We will prove that for Banach spaces verifying certain conditions, the complete interpolation sets are precisely the minimal stable sampling sets and are also the maximal stable interpolation sets. Finally we illustrate these results applying them to Paley-Wiener spaces, where we use a result by B. Matei, Yves Meyer and J. Ortega-Cerd´a based on the celebrated Fefferman theorem.
References
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