Algebra of Bergman Operators with Automorphic Coefficients and Parabolic Group of Shifts
UDC 517.983 We study the algebra of operators with the Bergman kernel extended by isometric weighted shift operators. The coefficients of the algebra are assumed to be automorphic with respect to a cyclic parabolic group of fractional-linear transformations of a unit disk and continuous on the Riem...
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| Datum: | 2001 |
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| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2001
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510468956749824 |
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| author | Mozel’, V. A. Chernetskii, V. A. Мозель, В. А. Чернецкий, В. А. Мозель, В. А. Чернецкий, В. А. |
| author_facet | Mozel’, V. A. Chernetskii, V. A. Мозель, В. А. Чернецкий, В. А. Мозель, В. А. Чернецкий, В. А. |
| author_sort | Mozel’, V. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:26:49Z |
| description | UDC 517.983
We study the algebra of operators with the Bergman kernel extended by isometric weighted shift operators. The coefficients of the algebra are assumed to be automorphic with respect to a cyclic parabolic group of fractional-linear transformations of a unit disk and continuous on the Riemann surface of the group. By using an isometric transformation, we obtain a quasiautomorphic matrix operator on the Riemann surface with properties similar to the properties of the Bergman operator. This enables us to construct the algebra of symbols, devise an efficient criterion for the Fredholm property, and calculate the index of the operators of the algebra considered. |
| first_indexed | 2026-03-24T02:57:29Z |
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| id | umjimathkievua-article-4340 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
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| language | rus English |
| last_indexed | 2026-03-24T02:57:29Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/af/1ceb85624ca21ce7193184d9af79ceaf.pdf |
| spelling | umjimathkievua-article-43402020-03-18T20:26:49Z Algebra of Bergman Operators with Automorphic Coefficients and Parabolic Group of Shifts Алгебра операторов Бергмана с автоморфными коэффициентами и параболической группой сдвигов Mozel’, V. A. Chernetskii, V. A. Мозель, В. А. Чернецкий, В. А. Мозель, В. А. Чернецкий, В. А. UDC 517.983 We study the algebra of operators with the Bergman kernel extended by isometric weighted shift operators. The coefficients of the algebra are assumed to be automorphic with respect to a cyclic parabolic group of fractional-linear transformations of a unit disk and continuous on the Riemann surface of the group. By using an isometric transformation, we obtain a quasiautomorphic matrix operator on the Riemann surface with properties similar to the properties of the Bergman operator. This enables us to construct the algebra of symbols, devise an efficient criterion for the Fredholm property, and calculate the index of the operators of the algebra considered. УДК 517.983 Вивчається алгебра операторів з ядром Бергмана, розширена ізометричними операторами зваженого зсуву. Коефіцієнти алгебри вважаються автоморфними відносно циклічної параболічної групи дробно-лінійних перетворень одиничного круга і неперервними на рімановій поверхні групи. За допомогою ізометричного перетворення одержано квазіавтоморфний матричний оператор на рімановій поверхні із властивостями, аналогічними властивостям оператора Бергмана. Це дає можливість побудувати алгебру символів, дати ефективний критерій фредгольмовості та обчислити індекс операторів розглянутої алгебри. Institute of Mathematics, NAS of Ukraine 2001-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4340 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 9 (2001); 1218-1223 Український математичний журнал; Том 53 № 9 (2001); 1218-1223 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4340/5384 https://umj.imath.kiev.ua/index.php/umj/article/view/4340/5385 Copyright (c) 2001 Mozel’ V. A.; Chernetskii V. A. |
| spellingShingle | Mozel’, V. A. Chernetskii, V. A. Мозель, В. А. Чернецкий, В. А. Мозель, В. А. Чернецкий, В. А. Algebra of Bergman Operators with Automorphic Coefficients and Parabolic Group of Shifts |
| title | Algebra of Bergman Operators with Automorphic Coefficients and Parabolic Group of Shifts |
| title_alt | Алгебра операторов Бергмана с автоморфными коэффициентами и параболической группой сдвигов |
| title_full | Algebra of Bergman Operators with Automorphic Coefficients and Parabolic Group of Shifts |
| title_fullStr | Algebra of Bergman Operators with Automorphic Coefficients and Parabolic Group of Shifts |
| title_full_unstemmed | Algebra of Bergman Operators with Automorphic Coefficients and Parabolic Group of Shifts |
| title_short | Algebra of Bergman Operators with Automorphic Coefficients and Parabolic Group of Shifts |
| title_sort | algebra of bergman operators with automorphic coefficients and parabolic group of shifts |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4340 |
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