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On boundedness of a function on a Zalcman domain. (English) Zbl 0969.30016

Summary: We consider boundedness of a function defined by an infinite product which is used to study a uniqueness theorem on a plane domain and the point separation problem of a two-sheeted covering Riemann surface. We show that there is such an infinite product that it converges but the function defined by it is not bounded on an arbitrary Zalcman domain.

MSC:

30D50 Blaschke products, etc. (MSC2000)
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References:

[1] Hayashi, M., and Nakai, M.: A uniqueness theorem and the Myrberg phenomenon. J. d’Analyse Math., 76 , 109-136 (1998). · Zbl 0977.30032
[2] Hayashi, M., Kobayashi, Y., and Nakai, M.: A Uniqueness Theorem and the Myrberg Phenomenon for a Zalcman Domain. J. d’Analyse Math., 82 , 267-283 (2000). · Zbl 0965.30024
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