We plan to demonstrate how the classical de Branges theory of Hilbert spaces of entire function can be extended to a more general setting of Cauchy–de Branges spaces. In particular,

new versions of de Branges Ordering Theorem for nearly invariant subspaces in Cauchy–de Branges spaces will be reviewed. Also, the localization of zeros in these spaces will be discussed.

This is joint work with A. Baranov and Yu. Belov.