On the chain structure of de Branges spaces

It is well known that any measure $\mu$ (with $\int(1+x^2)^{-1}d\mu(x)<\infty$) on the real line generates a chain of Hilbert spaces of entire functions (de Branges spaces). These spaces are isometrically embedded in $L^2(\mu)$. We study the indivisible intervals and the stability of exponential type in the chains of de Branges subspaces in terms of the spectral measure.
The talk is based on joint work with Alexander Borichev (Aix-Marseille University).