Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions
A bundle of differential operators $$\mathcal{L}(\lambda ),\lambda \in \mathbb{C}:\mathcal{L}(\lambda )y(x) = y^{(4)} (x) - 2\lambda ^2 y^{(2)} (x) + \lambda ^4 y(x),|x| \leqslant 1,y( \pm 1) = y\prime ( \pm 1) = 0,$$ is considered. In various function spaces, we establish the facts about the expan...
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| Дата: | 1993 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1993
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5967 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512190971248640 |
|---|---|
| author | Gomilko, A. M. Гомилко, А. М. Гомилко, А. М. |
| author_facet | Gomilko, A. M. Гомилко, А. М. Гомилко, А. М. |
| author_sort | Gomilko, A. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:22:20Z |
| description | A bundle of differential operators
$$\mathcal{L}(\lambda ),\lambda \in \mathbb{C}:\mathcal{L}(\lambda )y(x) = y^{(4)} (x) - 2\lambda ^2 y^{(2)} (x) + \lambda ^4 y(x),|x| \leqslant 1,y( \pm 1) = y\prime ( \pm 1) = 0,$$
is considered. In various function spaces, we establish the facts about the expansions of a pair of functions $f(x)$ and $g(x)$ in the system $\{y_k (x),\; iλ_k y_k (x)|}_{k=1}^{ ∞}$, where $y_k(x), k = 1,2,...,$ are the eigenfunctions of the bundle $L (λ)$ corresponding to the eigenvalues $λ_k$, with $\Im λ_k > 0$. |
| first_indexed | 2026-03-24T03:24:51Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5967 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:24:51Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/9e/d8874e2ff3de5d3184fe88f349b1e99e.pdf |
| spelling | umjimathkievua-article-59672020-03-19T09:22:20Z Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions Разложение по части собственных функций пучка дифференциальных операторов четвертого порядка Gomilko, A. M. Гомилко, А. М. Гомилко, А. М. A bundle of differential operators $$\mathcal{L}(\lambda ),\lambda \in \mathbb{C}:\mathcal{L}(\lambda )y(x) = y^{(4)} (x) - 2\lambda ^2 y^{(2)} (x) + \lambda ^4 y(x),|x| \leqslant 1,y( \pm 1) = y\prime ( \pm 1) = 0,$$ is considered. In various function spaces, we establish the facts about the expansions of a pair of functions $f(x)$ and $g(x)$ in the system $\{y_k (x),\; iλ_k y_k (x)|}_{k=1}^{ ∞}$, where $y_k(x), k = 1,2,...,$ are the eigenfunctions of the bundle $L (λ)$ corresponding to the eigenvalues $λ_k$, with $\Im λ_k > 0$. Розглядається жмуток диференціальних операторів $$\mathcal{L}(\lambda ),\lambda \in \mathbb{C}:\mathcal{L}(\lambda )y(x) = y^{(4)} (x) - 2\lambda ^2 y^{(2)} (x) + \lambda ^4 y(x),|x| \leqslant 1,y( \pm 1) = y\prime ( \pm 1) = 0.$$ Одержані результати про розклад у різних функціональних просторах пари функцій $f(x)$, $g(x)$ засистемою $\{y_k (x),\; iλ_k y_k (x)|}_{k=1}^{ ∞}$, де $y_k(x), k = 1,2,...,$, — власні функції жмутка $λ_k$, що відповідають власним значенням $λ_k$ з $\Im λ_k > 0$. Institute of Mathematics, NAS of Ukraine 1993-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5967 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 12 (1993); 1601–1612 Український математичний журнал; Том 45 № 12 (1993); 1601–1612 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5967/8617 https://umj.imath.kiev.ua/index.php/umj/article/view/5967/8618 Copyright (c) 1993 Gomilko A. M. |
| spellingShingle | Gomilko, A. M. Гомилко, А. М. Гомилко, А. М. Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions |
| title | Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions |
| title_alt | Разложение по части собственных функций пучка дифференциальных операторов четвертого порядка |
| title_full | Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions |
| title_fullStr | Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions |
| title_full_unstemmed | Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions |
| title_short | Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions |
| title_sort | expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5967 |
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