ON PRESENTATION OF GELFOND—LEONTIEV OPERATORS OF GENERALIZED DIFFERENTIATION IN SIMPLY CONNECTED REGION
Some new properties of the multiplier are determined. A class of simply connected regions whose multiplier is a connected set is described. This class is characterized by the availability of spirals in a multiplier. Let the Gelfond—Leontiev generalized differentiation operator be continuous in the s...
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| Format: | Article |
| Language: | Russian |
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Don State Technical University
2014-06-01
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| Series: | Advanced Engineering Research |
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| Online Access: | https://www.vestnik-donstu.ru/jour/article/view/306 |
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| _version_ | 1849408923674607616 |
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| author | Alexander Vasilyevich Bratishchev |
| author_facet | Alexander Vasilyevich Bratishchev |
| author_sort | Alexander Vasilyevich Bratishchev |
| collection | DOAJ |
| description | Some new properties of the multiplier are determined. A class of simply connected regions whose multiplier is a connected set is described. This class is characterized by the availability of spirals in a multiplier. Let the Gelfond—Leontiev generalized differentiation operator be continuous in the space of the analytic functions in simply connected region G of a complex plane. It is known to be presented as an operator of general complex convolution. The convolution kernel is generated by the many-valued function of one variable. The set M(G) with the property M(G)·G⊆G is called multiplier G. Let the region multiplier be connected, and it does not align with identity. It is proved in the paper that the functions under consideration will be univalent under these conditions. If multiplier G is unconnected, then there is always a generalized differentiation Gelfond—Leontiev operator with a many-valued generating function. |
| format | Article |
| id | doaj-art-0f39708e396a4170883ca07bbaaba844 |
| institution | Kabale University |
| issn | 2687-1653 |
| language | Russian |
| publishDate | 2014-06-01 |
| publisher | Don State Technical University |
| record_format | Article |
| series | Advanced Engineering Research |
| spelling | doaj-art-0f39708e396a4170883ca07bbaaba8442025-08-20T03:35:40ZrusDon State Technical UniversityAdvanced Engineering Research2687-16532014-06-01142212710.12737/4536299ON PRESENTATION OF GELFOND—LEONTIEV OPERATORS OF GENERALIZED DIFFERENTIATION IN SIMPLY CONNECTED REGIONAlexander Vasilyevich Bratishchev0Don State Technical University, RussiaSome new properties of the multiplier are determined. A class of simply connected regions whose multiplier is a connected set is described. This class is characterized by the availability of spirals in a multiplier. Let the Gelfond—Leontiev generalized differentiation operator be continuous in the space of the analytic functions in simply connected region G of a complex plane. It is known to be presented as an operator of general complex convolution. The convolution kernel is generated by the many-valued function of one variable. The set M(G) with the property M(G)·G⊆G is called multiplier G. Let the region multiplier be connected, and it does not align with identity. It is proved in the paper that the functions under consideration will be univalent under these conditions. If multiplier G is unconnected, then there is always a generalized differentiation Gelfond—Leontiev operator with a many-valued generating function.https://www.vestnik-donstu.ru/jour/article/view/306multiplier of a region generalized gelfond—leontiev derivative, operator kernel. |
| spellingShingle | Alexander Vasilyevich Bratishchev ON PRESENTATION OF GELFOND—LEONTIEV OPERATORS OF GENERALIZED DIFFERENTIATION IN SIMPLY CONNECTED REGION Advanced Engineering Research multiplier of a region generalized gelfond—leontiev derivative, operator kernel. |
| title | ON PRESENTATION OF GELFOND—LEONTIEV OPERATORS OF GENERALIZED DIFFERENTIATION IN SIMPLY CONNECTED REGION |
| title_full | ON PRESENTATION OF GELFOND—LEONTIEV OPERATORS OF GENERALIZED DIFFERENTIATION IN SIMPLY CONNECTED REGION |
| title_fullStr | ON PRESENTATION OF GELFOND—LEONTIEV OPERATORS OF GENERALIZED DIFFERENTIATION IN SIMPLY CONNECTED REGION |
| title_full_unstemmed | ON PRESENTATION OF GELFOND—LEONTIEV OPERATORS OF GENERALIZED DIFFERENTIATION IN SIMPLY CONNECTED REGION |
| title_short | ON PRESENTATION OF GELFOND—LEONTIEV OPERATORS OF GENERALIZED DIFFERENTIATION IN SIMPLY CONNECTED REGION |
| title_sort | on presentation of gelfond leontiev operators of generalized differentiation in simply connected region |
| topic | multiplier of a region generalized gelfond—leontiev derivative, operator kernel. |
| url | https://www.vestnik-donstu.ru/jour/article/view/306 |
| work_keys_str_mv | AT alexandervasilyevichbratishchev onpresentationofgelfondleontievoperatorsofgeneralizeddifferentiationinsimplyconnectedregion |