Abstract
We give new characterizations of the subsets S of the unit disc D of the complex plane such that the topology of the space A −∞ of holomorphic functions of polynomial growth on D coincides with the topology of space of the restrictions of the functions to the set S. These sets are called weakly sufficient sets for A −∞. Our approach is based on a study of the so-called ( p, q)-sampling sets which generalize the A − p -sampling sets of Seip. A characterization of ( p, q)-sampling and weakly sufficient rotation invariant sets is included. It permits us to obtain new examples and to solve an open question of Khôi and Thomas.
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