Generalized Vandermonde operator and bounded solutions of differential equations
UDC 517.929.2 We study the problem of existence of a unique bounded solution to a linear differential equation of any order with bounded operator coefficients. We consider the case where the corresponding ``algebraic'' operator equation has multiple separated pairwise commuting...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8984 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513351803600896 |
|---|---|
| author | Horodnii, M. Городній, Михайло |
| author_facet | Horodnii, M. Городній, Михайло |
| author_sort | Horodnii, M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-22T13:31:25Z |
| description | UDC 517.929.2
We study the problem of existence of a unique bounded solution to a linear differential equation of any order with bounded operator coefficients. We consider the case where the corresponding ``algebraic'' operator equation has multiple separated pairwise commuting roots. By using the generalized Vandermonde operator constructed with the help of these roots, we obtain a representation of the unique bounded solution. |
| doi_str_mv | 10.3842/umzh.v77i6.8984 |
| first_indexed | 2026-03-24T03:43:18Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-8984 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T03:43:18Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/c9/09b4f949edb9440050036d88c2ebe9c9 |
| spelling | umjimathkievua-article-89842026-03-22T13:31:25Z Generalized Vandermonde operator and bounded solutions of differential equations Узагальнений оператор Вандермонда й обмежені розв'язки диференціальних рівнянь Horodnii, M. Городній, Михайло generalized Vandermonde operator, differential equation, operator coefficient, bounded solutions узагальнений оператор Вандермонда, диференціальне рівняння, операторний коефіцієнт, обмежені розв'язки UDC 517.929.2 We study the problem of existence of a unique bounded solution to a linear differential equation of any order with bounded operator coefficients. We consider the case where the corresponding ``algebraic'' operator equation has multiple separated pairwise commuting roots. By using the generalized Vandermonde operator constructed with the help of these roots, we obtain a representation of the unique bounded solution. УДК 517.929.2 Вивчається питання про існування єдиного обмеженого розв'язку лінійного диференціального рівняння довільного порядку з обмеженими операторними коефіцієнтами. Розглянуто випадок, коли відповідне ,,алгебраїчне'' операторне рівняння має кратні, розділені, попарно комутовні корені. За допомогою узагальненого оператора Вандермонда, побудованого за такими коренями, отримано зображення єдиного обмеженого розв'язку. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8984 10.3842/umzh.v77i6.8984 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 6 (2025); 375–385 Український математичний журнал; Том 77 № 6 (2025); 375–385 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/8984/10541 Copyright (c) 2025 M. Horodnii |
| spellingShingle | Horodnii, M. Городній, Михайло Generalized Vandermonde operator and bounded solutions of differential equations |
| title | Generalized Vandermonde operator and bounded solutions of differential equations |
| title_alt | Узагальнений оператор Вандермонда й обмежені розв'язки диференціальних рівнянь |
| title_full | Generalized Vandermonde operator and bounded solutions of differential equations |
| title_fullStr | Generalized Vandermonde operator and bounded solutions of differential equations |
| title_full_unstemmed | Generalized Vandermonde operator and bounded solutions of differential equations |
| title_short | Generalized Vandermonde operator and bounded solutions of differential equations |
| title_sort | generalized vandermonde operator and bounded solutions of differential equations |
| topic_facet | generalized Vandermonde operator differential equation operator coefficient bounded solutions узагальнений оператор Вандермонда диференціальне рівняння операторний коефіцієнт обмежені розв'язки |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8984 |
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