Absolute values and real parts for functions in the smirnov class |
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Authors: | Takahiko Nakazi |
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Affiliation: | Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan |
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Abstract: | Let N+ denote the Smirnov class on the open unit disc D. It is easy to see that for any outer function g in N+, there exists a function G in N+ such that |g|; ≤ ReG on δ. We describe such a G. In general, G may not be outer. In this paper, a necessary and sufficient condition on g is given for the existence of an outer function G such that |;g|; < ReG. When g belongs to the Hardy space H1, G is trivially given as the Herglotz integral of |;g|;. |
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