Interpolation on the complex Hilbert sphere using positive definite and conditionally negative definite kernels
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 \[ L_E:=\text{span}\{g(\langle\cdot ,w\rangle):w \in E\}. \]
scientific article; zbMATH DE number 1354876