Open AccessIrregular stable sampling and interpolation in functional normed spaces
Author(s) -
José Alfonso López Nicolás
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.45497
Subject(s) - interpolation (computer graphics) , mathematics , banach space , interpolation space , set (abstract data type) , sampling (signal processing) , space (punctuation) , uniqueness , pure mathematics , discrete mathematics , mathematical analysis , functional analysis , computer science , artificial intelligence , filter (signal processing) , motion (physics) , biochemistry , chemistry , computer vision , gene , programming language , operating system
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.