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- W80490114 abstract "We consider a function /O) meromorphic and single-valued in a g-ply connected domain D, and denote by n(w) and «i(to) the numbers of zu-points of /(#) and/'(«) respectively in D. Lemma 1. Let D be a domain whose boundary consists of finite number of closed Jordan curves. Let /(») be meromorphic and single-valued in the closure of D and continuous on the boundary. If there exists a direction such that every straight line parallel to it cuts at most 2P times the image curve by /(s) of the boundary ofD, then the minimum value of nQw~) is at least max(«(°o)-p, 0), and the maximumvalue of rc(w) is at most w(oo)+/>. This lemma can be proved in the same way as by Umezawa CO, and so the proof may be omitted. Lemma 2. Let F be a set offinite number of closed smooth curves on the w-plane, and let" @default.
- W80490114 created "2016-06-24" @default.
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- W80490114 date "1957-12-15" @default.
- W80490114 modified "2023-09-23" @default.
- W80490114 title "On the Multivalency of Meromorphic Functions in a Multiply Connected Domain" @default.
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