Multipliers for entire functions and an interpolation problem of Beurling
Let \(B_\tau\) be the set of all entire functions of exponential type at most \(\tau\) whose restriction to the real line belong to \(L^\infty(R)\) and let \(\Lambda=\{\lambda_k\}\) be a sequence of distinct points in \(\mathbb{C}\) such that for any \(\{a_k\}\), \(\sup_k| a_k| e^{-\tau|{\mathfrak F} \lambda_k|} <\infty\), the interpolation problem \(f(\lambda_k)=a_k\) has a solution \(f\in B_\tau\), i.e. \(\Lambda\) is an interpolating sequence for \(B_\tau\). The authors prove the criterion of the interpolating sequence for \(B_\tau\).
scientific article; zbMATH DE number 1274806
scientific article