Separated sequences and interpolation
Volume 274 / 2024
Studia Mathematica 274 (2024), 79-99
MSC: Primary 26E10; Secondary 41A05, 46F10
DOI: 10.4064/sm230620-11-10
Published online: 3 January 2024
Abstract
We introduce the notion of -separated increasing sequences \{ x_{n}\} _{n=1}^{\infty }. We establish that interpolation problems of the kind \varphi ( x_{n}) =z_{n} have solutions \varphi \in \mathcal {S}( \mathbb {R}) for all sequences \{ z_{n}\} of rapid decay in the sense that z_{n}=o( x_{n}^{-\alpha }) for all \alpha \gt 0 if and only if \{ x_{n}\} is \nu -separated for some \nu . We also give several generalizations of this result.
