Zeros of entire functions of finite order
<p/> <p>Given <inline-formula><graphic file="1029-242X-2002-216747-i1.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2002-216747-i2.gif"/></inline-formula>, let <inline-formula><graphic file="1029-24...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2002-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/7/216747 |
| _version_ | 1819131733023391744 |
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| author | Supper Raphaële |
| author_facet | Supper Raphaële |
| author_sort | Supper Raphaële |
| collection | DOAJ |
| description | <p/> <p>Given <inline-formula><graphic file="1029-242X-2002-216747-i1.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2002-216747-i2.gif"/></inline-formula>, let <inline-formula><graphic file="1029-242X-2002-216747-i3.gif"/></inline-formula> be the set of all entire functions <inline-formula><graphic file="1029-242X-2002-216747-i4.gif"/></inline-formula>, with <inline-formula><graphic file="1029-242X-2002-216747-i5.gif"/></inline-formula>, for which there exists some constant <inline-formula><graphic file="1029-242X-2002-216747-i6.gif"/></inline-formula> such that <inline-formula><graphic file="1029-242X-2002-216747-i7.gif"/></inline-formula>. It is shown that the zero set <inline-formula><graphic file="1029-242X-2002-216747-i8.gif"/></inline-formula> of a function of <inline-formula><graphic file="1029-242X-2002-216747-i9.gif"/></inline-formula> satisfies <inline-formula><graphic file="1029-242X-2002-216747-i10.gif"/></inline-formula> and that the union of the zero sets of two functions of <inline-formula><graphic file="1029-242X-2002-216747-i11.gif"/></inline-formula> is not necessarily the zero set of a function of <inline-formula><graphic file="1029-242X-2002-216747-i12.gif"/></inline-formula>. Some uniqueness results of Carlson's type are also obtained.</p> |
| first_indexed | 2024-12-22T09:20:11Z |
| format | Article |
| id | doaj.art-0402403ebd5a46ba8258d482343bcdb9 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-22T09:20:11Z |
| publishDate | 2002-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-0402403ebd5a46ba8258d482343bcdb92022-12-21T18:31:13ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2002-01-0120021216747Zeros of entire functions of finite orderSupper Raphaële<p/> <p>Given <inline-formula><graphic file="1029-242X-2002-216747-i1.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2002-216747-i2.gif"/></inline-formula>, let <inline-formula><graphic file="1029-242X-2002-216747-i3.gif"/></inline-formula> be the set of all entire functions <inline-formula><graphic file="1029-242X-2002-216747-i4.gif"/></inline-formula>, with <inline-formula><graphic file="1029-242X-2002-216747-i5.gif"/></inline-formula>, for which there exists some constant <inline-formula><graphic file="1029-242X-2002-216747-i6.gif"/></inline-formula> such that <inline-formula><graphic file="1029-242X-2002-216747-i7.gif"/></inline-formula>. It is shown that the zero set <inline-formula><graphic file="1029-242X-2002-216747-i8.gif"/></inline-formula> of a function of <inline-formula><graphic file="1029-242X-2002-216747-i9.gif"/></inline-formula> satisfies <inline-formula><graphic file="1029-242X-2002-216747-i10.gif"/></inline-formula> and that the union of the zero sets of two functions of <inline-formula><graphic file="1029-242X-2002-216747-i11.gif"/></inline-formula> is not necessarily the zero set of a function of <inline-formula><graphic file="1029-242X-2002-216747-i12.gif"/></inline-formula>. Some uniqueness results of Carlson's type are also obtained.</p>http://www.journalofinequalitiesandapplications.com/content/7/216747Entire holomorphic functionsOrder of growthZeros |
| spellingShingle | Supper Raphaële Zeros of entire functions of finite order Journal of Inequalities and Applications Entire holomorphic functions Order of growth Zeros |
| title | Zeros of entire functions of finite order |
| title_full | Zeros of entire functions of finite order |
| title_fullStr | Zeros of entire functions of finite order |
| title_full_unstemmed | Zeros of entire functions of finite order |
| title_short | Zeros of entire functions of finite order |
| title_sort | zeros of entire functions of finite order |
| topic | Entire holomorphic functions Order of growth Zeros |
| url | http://www.journalofinequalitiesandapplications.com/content/7/216747 |
| work_keys_str_mv | AT supperrapha235le zerosofentirefunctionsoffiniteorder |