Interpolating sequences of complex hyperplanes in the unit ball of \({\mathbb{C}}^ n\)
A sufficient condition is given to make a sequence \(L_ j\) of complex hyperplanes in the unit ball \(B^ n\subseteq {\mathbb{C}}^ n\) an interpolating sequence for \(H^{\infty}\), i.e. given holomorphic functions \(f_ j\) defined on each hyperplane of the sequence, \(\| f_ j\|_{\infty}\leq 1\), there exists a function \(f\in H^{\infty}(B^ n)\) such that \(f|_{L_ j}=f_ j.\) Comparisons are made with results concerning interpolating sequences of points; the exponent in Varopoulos' necessary condition for interpolating sequences of points is shown to be sharp even for sequences of hyperplanes.
interpolating sequence for \(H^{\infty }\)
scientific article; zbMATH DE number 3901150
scientific article