## 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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