Some unsolved problems on meromorphic functions of uniformly bounded characteristic
The family UBC(R) of meromorphic functions of uniformly bounded characteristic in a Rieman surface R is defined in terms of the Shimizu-Ahlfors characteristic function. There are some natural parallels between UBC(R) and BMOA(R), the family of holomorphic functions of bounded mean oscillation in R....
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000527 |
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| _version_ | 1832547965274685440 |
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| author | Shinji Yamashita |
| author_facet | Shinji Yamashita |
| author_sort | Shinji Yamashita |
| collection | DOAJ |
| description | The family UBC(R) of meromorphic functions of uniformly bounded characteristic in a Rieman surface R is defined in terms of the Shimizu-Ahlfors characteristic function. There are some natural parallels between UBC(R) and BMOA(R), the family of holomorphic functions of bounded mean oscillation in R. After a survey some open problems are proposed in contrast with BMOA(R). |
| format | Article |
| id | doaj-art-141fd55797ad4b008c9bc58793fa1e03 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-141fd55797ad4b008c9bc58793fa1e032025-02-03T06:42:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018347748210.1155/S0161171285000527Some unsolved problems on meromorphic functions of uniformly bounded characteristicShinji Yamashita0Department of Mathematics, Tokyo Metropolitan University, Fukasawa, Setagaya, Tokyo 158, JapanThe family UBC(R) of meromorphic functions of uniformly bounded characteristic in a Rieman surface R is defined in terms of the Shimizu-Ahlfors characteristic function. There are some natural parallels between UBC(R) and BMOA(R), the family of holomorphic functions of bounded mean oscillation in R. After a survey some open problems are proposed in contrast with BMOA(R).http://dx.doi.org/10.1155/S0161171285000527Riemann surfaceShimizu-Ahlfors' characteristic functionUBC(R)BMOA(R)harmonic majorantF. Riesz' decompositionCarleson measureclassification of Riemann surfaces. |
| spellingShingle | Shinji Yamashita Some unsolved problems on meromorphic functions of uniformly bounded characteristic International Journal of Mathematics and Mathematical Sciences Riemann surface Shimizu-Ahlfors' characteristic function UBC(R) BMOA(R) harmonic majorant F. Riesz' decomposition Carleson measure classification of Riemann surfaces. |
| title | Some unsolved problems on meromorphic functions of uniformly bounded characteristic |
| title_full | Some unsolved problems on meromorphic functions of uniformly bounded characteristic |
| title_fullStr | Some unsolved problems on meromorphic functions of uniformly bounded characteristic |
| title_full_unstemmed | Some unsolved problems on meromorphic functions of uniformly bounded characteristic |
| title_short | Some unsolved problems on meromorphic functions of uniformly bounded characteristic |
| title_sort | some unsolved problems on meromorphic functions of uniformly bounded characteristic |
| topic | Riemann surface Shimizu-Ahlfors' characteristic function UBC(R) BMOA(R) harmonic majorant F. Riesz' decomposition Carleson measure classification of Riemann surfaces. |
| url | http://dx.doi.org/10.1155/S0161171285000527 |
| work_keys_str_mv | AT shinjiyamashita someunsolvedproblemsonmeromorphicfunctionsofuniformlyboundedcharacteristic |