ON ASYMPTOTIC VALUES OF FUNCTIONS IN A POLYDISK DOMAIN AND BAGEMIHL’S THEOREM
Asymptotic sets of functions in a polydisk domain of arbitrary connectivity are studied. We construct an example of such function, having preassigned asymptotic set. This result generalizes well-known examples, obtained by M. Heins and W. Gross for entire functions. Moreover, it is found out that no...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Petrozavodsk State University
2015-12-01
|
| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=2951&lang=en |
| id |
doaj-d85fb73cb22a49ddbe4db267ad85dfb4 |
|---|---|
| record_format |
Article |
| spelling |
doaj-d85fb73cb22a49ddbe4db267ad85dfb42021-07-02T05:42:14ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322015-12-014 (22)2233110.15393/j3.art.2015.2951ON ASYMPTOTIC VALUES OF FUNCTIONS IN A POLYDISK DOMAIN AND BAGEMIHL’S THEOREME. G. Ganenkova0Petrozavodsk State UniversityAsymptotic sets of functions in a polydisk domain of arbitrary connectivity are studied. We construct an example of such function, having preassigned asymptotic set. This result generalizes well-known examples, obtained by M. Heins and W. Gross for entire functions. Moreover, it is found out that not all results on asymptotic sets of functions in C can be extended to functions in C^n. In particular, this fact is connected with the failure of Bagemihl's theorem on ambiguous points for functions in R^n, n≥3.http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=2951&lang=enanalytic setambiguous pointasymptotic value |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
E. G. Ganenkova |
| spellingShingle |
E. G. Ganenkova ON ASYMPTOTIC VALUES OF FUNCTIONS IN A POLYDISK DOMAIN AND BAGEMIHL’S THEOREM Проблемы анализа analytic set ambiguous point asymptotic value |
| author_facet |
E. G. Ganenkova |
| author_sort |
E. G. Ganenkova |
| title |
ON ASYMPTOTIC VALUES OF FUNCTIONS IN A POLYDISK DOMAIN AND BAGEMIHL’S THEOREM |
| title_short |
ON ASYMPTOTIC VALUES OF FUNCTIONS IN A POLYDISK DOMAIN AND BAGEMIHL’S THEOREM |
| title_full |
ON ASYMPTOTIC VALUES OF FUNCTIONS IN A POLYDISK DOMAIN AND BAGEMIHL’S THEOREM |
| title_fullStr |
ON ASYMPTOTIC VALUES OF FUNCTIONS IN A POLYDISK DOMAIN AND BAGEMIHL’S THEOREM |
| title_full_unstemmed |
ON ASYMPTOTIC VALUES OF FUNCTIONS IN A POLYDISK DOMAIN AND BAGEMIHL’S THEOREM |
| title_sort |
on asymptotic values of functions in a polydisk domain and bagemihl’s theorem |
| publisher |
Petrozavodsk State University |
| series |
Проблемы анализа |
| issn |
2306-3424 2306-3432 |
| publishDate |
2015-12-01 |
| description |
Asymptotic sets of functions in a polydisk domain of arbitrary connectivity are studied. We construct an example of such function, having preassigned asymptotic set. This result generalizes well-known examples, obtained by M. Heins and W. Gross for entire functions. Moreover, it is found out that not all results on asymptotic sets of functions in C can be extended to functions in C^n. In particular, this fact is connected with the failure of Bagemihl's theorem on ambiguous points for functions in R^n, n≥3. |
| topic |
analytic set ambiguous point asymptotic value |
| url |
http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=2951&lang=en |
| work_keys_str_mv |
AT egganenkova onasymptoticvaluesoffunctionsinapolydiskdomainandbagemihlstheorem |
| _version_ |
1721338328251367424 |