Abstract. A de Branges space is a reproducing kernel Hilbert space of entire functions which satisfies additional axioms. We consider such de Branges spaces whose elements possess a certain growth behaviour (e.g. are all of exponential type) and investigate the interplay of Hilbert space structure and growth behaviour. We characterize the presence of certain growth behaviour, prove the existence of spaces with prescribed growth and investigate the structure of subspaces defined by growth restrictions.

AMS Subject Classification (1991): 46E20, 30D15, 46E22

Keyword(s): de Branges space, growth function, exponential type

Received March 23, 2004, and in revised form March 7, 2005. (Registered under 5868/2009.)