Abstract
This paper gives conditions on the behavior of a sequence of holomorphic functions {fk(z)} and a strictly increasing sequence of positive integers {mk} that assures the infinite product \({\Pi f_k(z^{m_k})}\) is strongly annular. A constructive proof is given that shows if the sequence {fk(z)} exhibits certain boundary behavior along with a uniform boundedness condition then a number p > 1 exists such that if {mk} satisfies mk+1/mk ≥ p then the above product is strongly annular.
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