EXTENSION OF STARLIKE FUNCTIONS TO A FINITELY PUNCTURED PLANE
We consider a sequence of functions which are starlike in the unit disk and their logarithmic derivatives are meromorphic with a finite number of simple poles in any boundary domain. These poles are either determined or random with given characteristics. The aim of the article is the limit proce...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Petrozavodsk State University
2017-06-01
|
| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3691&lang=en |
| _version_ | 1818613787008172032 |
|---|---|
| author | D. V. Prokhorov |
| author_facet | D. V. Prokhorov |
| author_sort | D. V. Prokhorov |
| collection | DOAJ |
| description | We consider a sequence of functions which are starlike
in the unit disk and their logarithmic derivatives are meromorphic
with a finite number of simple poles in any boundary
domain. These poles are either determined or random with given
characteristics. The aim of the article is the limit process and
the properties of limit functions. We distinguish conditions for
residues and distribution of poles. Under certain conditions, the
sequence converges to the identity function. Another conditions
allow us to obtain estimates for the limit function and its logarithmic
derivative. |
| first_indexed | 2024-12-16T16:07:40Z |
| format | Article |
| id | doaj.art-8b54fcd9db164b628972068710e9108f |
| institution | Directory Open Access Journal |
| issn | 2306-3424 2306-3432 |
| language | English |
| last_indexed | 2024-12-16T16:07:40Z |
| publishDate | 2017-06-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj.art-8b54fcd9db164b628972068710e9108f2022-12-21T22:25:19ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322017-06-016(24)110.15393/j3.art.2017.3691EXTENSION OF STARLIKE FUNCTIONS TO A FINITELY PUNCTURED PLANED. V. Prokhorov0Saratov State UniversityWe consider a sequence of functions which are starlike in the unit disk and their logarithmic derivatives are meromorphic with a finite number of simple poles in any boundary domain. These poles are either determined or random with given characteristics. The aim of the article is the limit process and the properties of limit functions. We distinguish conditions for residues and distribution of poles. Under certain conditions, the sequence converges to the identity function. Another conditions allow us to obtain estimates for the limit function and its logarithmic derivative.http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3691&lang=enstarlike functionmeromorphic functionweightdeterministic point regulationuniform distribution |
| spellingShingle | D. V. Prokhorov EXTENSION OF STARLIKE FUNCTIONS TO A FINITELY PUNCTURED PLANE Проблемы анализа starlike function meromorphic function weight deterministic point regulation uniform distribution |
| title | EXTENSION OF STARLIKE FUNCTIONS TO A FINITELY PUNCTURED PLANE |
| title_full | EXTENSION OF STARLIKE FUNCTIONS TO A FINITELY PUNCTURED PLANE |
| title_fullStr | EXTENSION OF STARLIKE FUNCTIONS TO A FINITELY PUNCTURED PLANE |
| title_full_unstemmed | EXTENSION OF STARLIKE FUNCTIONS TO A FINITELY PUNCTURED PLANE |
| title_short | EXTENSION OF STARLIKE FUNCTIONS TO A FINITELY PUNCTURED PLANE |
| title_sort | extension of starlike functions to a finitely punctured plane |
| topic | starlike function meromorphic function weight deterministic point regulation uniform distribution |
| url | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3691&lang=en |
| work_keys_str_mv | AT dvprokhorov extensionofstarlikefunctionstoafinitelypuncturedplane |