On the nonexistence of a continuous linear operator of a certain form from S to H(D)
Let D be a domain in the complex plane and \(\{a_ k\}\subset D\)- a fixed sequence of distinct points with no points of accumulation in D. Let S be the space of all sequences with coordinate convergence and H(D) be the space of all holomorphic functions on D with topology of uniform convergence on compact subsets. Theorem. There does not exist a continuous operator A from S into H(D) such that \(A(\{b_ k\})=f_ b(z)\), where \(f_ b(a_ k)=b_ k\) (k\(\geq 1).\) This result can be related to interpolation in spaces of holomorphic functions.
interpolation in spaces of holomorphic functions
scientific article; zbMATH DE number 4200921