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A uniqueness theorem and the myrberg phenomenon for a Zalcman domain
| Title: | A uniqueness theorem and the myrberg phenomenon for a Zalcman domain |
| Authors: | Hayashi, Mikihiro Browse this author →KAKEN DB | | Kobayashi, Yasuyuki Browse this author | | Nakai, Mitsuru Browse this author |
| Issue Date: | 2000 |
| Publisher: | Springer |
| Journal Title: | Journal d'Analyse Mathématique |
| Volume: | 82 |
| Issue: | 1 |
| Start Page: | 267 |
| End Page: | 283 |
| Publisher DOI: | 10.1007/BF02791230 |
| Abstract: | LetR=Δ0\∪nΔn be a Zalcman domain (or L-domain), where Δ0 : 0<|z| <1, Δn : |z-c n|≤r n,cn ↘0, Δn ⊂ Δ0 and Δn ∩ Δm= φ(n≠m). 0217 0115 V 3 For an unlimited two-sheeted covering R = φ-1 (R) with the branch points {φ-1(c n)}, set R = φ-1 (R). In the casec n=2−n , it was proved that if a uniqueness theorem is valid forH ∞ (R) atz=0, then the Myrberg phenomenon H∞(R) oφ = H∞ (R) occurs. One might suspect that the converse also holds. In this paper, contrary to this intuition, we show that the converse of this previous result is not true. In addition, we generalize the previous result for more general sequences {c n}. By this generalization we can even partly simplify the previous proof. |
| Rights: | The original publication is available at www.springerlink.com |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/43861 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 林 実樹廣
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