Hermitian indefinite functions and pontryagin spaces of entire functions

We establish and investigate a connection between hermitian indefinite cont inuous functions with finitely many negative squares defined on a finite in terval and so-called de Branges spaces of entire functions. This enables us to relate to any hermitian indefinite continuous function on the real axis a certain chain of 2 x 2-matrix valued entire functions, which are in the positive definite case tightly connected with canonical systems of differen tial equations.