Interpolation on the complex Hilbert sphere using positive definite and conditionally negative definite kernels
type: Item
instance of: scholarly article
title: Interpolation on the complex Hilbert sphere using positive definite and conditionally negative definite kernels
zbMATH Open document ID: 0928.65065
DOI: 10.1023/A:1006599221736
published in: Acta Mathematica Hungarica
publication date: 1999-10-31T00:00:00Z
review text: Let \(S^\infty\) be the unit sphere of the complex Hilbert space \(\ell^2\). Given any finite subset \(E\) of \(S^\infty\), we show how to construct large classes of continuous functions \(g\) defined on the unit disk \(\overline{\Delta(0,1)}:=\{\zeta\in \mathbb{C}:| \zeta| \leqq 1\}\) that solve the problem of interpolating arbitrary data on \(E\) by a function in the linear space \[ L_E:=\text{span}\{g(\langle\cdot ,w\rangle):w \in E\}. \]
Mathematics Subject Classification ID: 65J05
Mathematics Subject Classification ID: 46B45
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 1354876
zbMATH Keywords: Hilbert sphere
zbMATH Keywords: interpolation
zbMATH Keywords: unit sphere
zbMATH Keywords: complex Hilbert space \(\ell^2\)
author: Valdir A. Menegatto
MaRDI profile type: Publication
full work available at URL: a:1006599221736
OpenAlex ID: W1810895151
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description: scientific article; zbMATH DE number 1354876