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We study the indivisible intervals and the monotonicity of the growth of theexponential type in the chains of de Branges subspaces in terms of the spectralmeasure. We prove that for spectral measures supported on $\mathbb Z$, thereexist at most two subspaces of the same type, which then bound an indivisibleinterval. Furthermore, in this case, we study possible locations of theindivisible intervals.

On the chain structure in the de Branges spaces