Abstract
Recent work has been concerned with Hilbert spaces whose elements are entire functions and which have these three properties: (HI) Whenever F(z) is in the space and has a nonreal zero w, the function F(z) (z 0)/(z w) is in the space and has the same norm as F(z). (H2) Whenever w is a nonreal number, the linear functional defined on the space by F(z) -, F(w) is continuous. (H3) Whenever F(z) is in the space, the function F*(z) = F(z) is in the space and has the same norm as F(z). If E(z) is an entire function which satisfies the inequality
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