Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation
In commutative associative third-rank algebras with principal identity over a complex field, we select bases such that hypercomplex monogenic functions constructed in these bases have components satisfying the three-dimensional Laplace equation. The notion of monogeneity for these functions is simil...
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| Date: | 2003 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4002 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510132893384704 |
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| author | Mel'nichenko, I. P. Мельниченко, И. П. Мельниченко, И. П. |
| author_facet | Mel'nichenko, I. P. Мельниченко, И. П. Мельниченко, И. П. |
| author_sort | Mel'nichenko, I. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:18:03Z |
| description | In commutative associative third-rank algebras with principal identity over a complex field, we select bases such that hypercomplex monogenic functions constructed in these bases have components satisfying the three-dimensional Laplace equation. The notion of monogeneity for these functions is similar to the notion of monogeneity in the complex plane. |
| first_indexed | 2026-03-24T02:52:09Z |
| format | Article |
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| id | umjimathkievua-article-4002 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:52:09Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/7a/8667c541e14522c338dc0a2bb148c07a.pdf |
| spelling | umjimathkievua-article-40022020-03-18T20:18:03Z Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation Алгебры функционально-инвариантных решений трехмерного уравнения Лапласа Mel'nichenko, I. P. Мельниченко, И. П. Мельниченко, И. П. In commutative associative third-rank algebras with principal identity over a complex field, we select bases such that hypercomplex monogenic functions constructed in these bases have components satisfying the three-dimensional Laplace equation. The notion of monogeneity for these functions is similar to the notion of monogeneity in the complex plane. У комутативних, асоціативних третього рангу алгебрах із головною одиницею над комплексним полем виділено такі базиси, що гіперкомплексні моногенні функції, побудовані в цих базисах, мають компоненти, що задовольняють тривимірне рівняння Лапласа. Поняття моногенності для цих функцій аналогічне поняттю моногенності в комплексній площині. Institute of Mathematics, NAS of Ukraine 2003-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4002 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 9 (2003); 1284-1290 Український математичний журнал; Том 55 № 9 (2003); 1284-1290 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4002/4716 https://umj.imath.kiev.ua/index.php/umj/article/view/4002/4717 Copyright (c) 2003 Mel'nichenko I. P. |
| spellingShingle | Mel'nichenko, I. P. Мельниченко, И. П. Мельниченко, И. П. Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation |
| title | Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation |
| title_alt | Алгебры функционально-инвариантных решений трехмерного
уравнения Лапласа |
| title_full | Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation |
| title_fullStr | Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation |
| title_full_unstemmed | Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation |
| title_short | Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation |
| title_sort | algebras of functionally invariant solutions of the three-dimensional laplace equation |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4002 |
| work_keys_str_mv | AT mel039nichenkoip algebrasoffunctionallyinvariantsolutionsofthethreedimensionallaplaceequation AT melʹničenkoip algebrasoffunctionallyinvariantsolutionsofthethreedimensionallaplaceequation AT melʹničenkoip algebrasoffunctionallyinvariantsolutionsofthethreedimensionallaplaceequation AT mel039nichenkoip algebryfunkcionalʹnoinvariantnyhrešenijtrehmernogouravneniâlaplasa AT melʹničenkoip algebryfunkcionalʹnoinvariantnyhrešenijtrehmernogouravneniâlaplasa AT melʹničenkoip algebryfunkcionalʹnoinvariantnyhrešenijtrehmernogouravneniâlaplasa |