Geodesic
Subspaces of de Branges spaces with prescribed growth
Algebra i analiz, Tome 18 (2006) no. 5, pp. 23-45.

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The growth properties of de Branges spaces and their subspaces are studied. It is shown that, for each given pair of growth functions $\lambda(r)=O(r)$ and $\lambda_1=o(\lambda)$, there exist de Branges spaces of growth $\lambda$ that have a de Branges subspace of growth $\lambda_1$. This phenomenon cannot occur for a class of de Branges spaces that, in a certain sense, behave regularly along the real axis.
Keywords: de Branges space, growth function, de Branges subspace. 
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A. Baranov; H. Woracek. Subspaces of de Branges spaces with prescribed growth. Algebra i analiz, Tome 18 (2006) no. 5, pp. 23-45. http://geodesic.mathdoc.fr/item/AA_2006_18_5_a1/

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