Some aspects of vector valued de Branges spaces of entire functions

Abstract

This paper deals with certain aspects of the vector valued de Branges spaces of entire functions that are based on pairs of Fredholm operator valued functions. Some factorization and isometric embedding results are extended from the scalar valued theory of de Branges spaces. In particular, global factorization of Fredholm operator valued entire functions and analytic equivalence of reproducing kernels of de Branges spaces are discussed. Additionally, the operator valued entire functions associated with these de Branges spaces are studied, and a connection with the operator nodes is established.