Sequences of Exponents in Constructing Strongly Annular Products

摘要

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