On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics
We obtain a formula for the expansion of an arbitrary function in a series in the eigenfunctions of the Sturm–Liouville boundary-value problem for the differential equation of cone functions. On the basis of this result, we derive a series of integral transformations (including well-known ones) and...
Збережено в:
| Дата: | 2001 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2001
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4301 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510431644221440 |
|---|---|
| author | Popov, G. Ya. Попов, Г. Я. |
| author_facet | Popov, G. Ya. Попов, Г. Я. |
| author_sort | Popov, G. Ya. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:59Z |
| description | We obtain a formula for the expansion of an arbitrary function in a series in the eigenfunctions of the Sturm–Liouville boundary-value problem for the differential equation of cone functions. On the basis of this result, we derive a series of integral transformations (including well-known ones) and inversion formulas for them. We apply these formulas to the solution of initial boundary-value problems in the theory of heat conduction for circular hollow cones truncated by spherical surfaces. |
| first_indexed | 2026-03-24T02:56:54Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4301 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:56:54Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5d/4968a236bc341ebb1df2ebd26727935d.pdf |
| spelling | umjimathkievua-article-43012020-03-18T20:25:59Z On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics О некоторых интегральных преобразованиях и об их применении к решению краевых задач математической физики Popov, G. Ya. Попов, Г. Я. We obtain a formula for the expansion of an arbitrary function in a series in the eigenfunctions of the Sturm–Liouville boundary-value problem for the differential equation of cone functions. On the basis of this result, we derive a series of integral transformations (including well-known ones) and inversion formulas for them. We apply these formulas to the solution of initial boundary-value problems in the theory of heat conduction for circular hollow cones truncated by spherical surfaces. Одержано формулу розкладу довільної' функції в ряд за власними функціями крайової задачі Штурма - Ліувілля для диференціального рівняння функцій конуса та на цій основі виведено серію інтегральних перетворень (в тому числі відомих) і формул обернення для них. Наведено застосування цих формул до розв'язання початково-крайових задач теорії теплопровідності для кругових порожнистих конусів, зрізаних сферичними поверхнями. Institute of Mathematics, NAS of Ukraine 2001-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4301 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 6 (2001); 810-819 Український математичний журнал; Том 53 № 6 (2001); 810-819 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4301/5306 https://umj.imath.kiev.ua/index.php/umj/article/view/4301/5307 Copyright (c) 2001 Popov G. Ya. |
| spellingShingle | Popov, G. Ya. Попов, Г. Я. On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics |
| title | On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics |
| title_alt | О некоторых интегральных преобразованиях и об их применении к решению краевых задач математической физики |
| title_full | On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics |
| title_fullStr | On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics |
| title_full_unstemmed | On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics |
| title_short | On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics |
| title_sort | on some integral transformations and their application to the solution of boundary-value problems in mathematical physics |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4301 |
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