Fourier method in the space of φB - distributions
In our previous articles, we introduced and explored the notion of φB -distributions with values in the Banach space. This offers a new perspective on the theory of solvability of linear problems, which is important for solving partial differential equations, especially equations with deviating argu...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2023-11-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/7 |
| _version_ | 1797205406382030848 |
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| author | V. S. Mokeichev A. M. Sidorov |
| author_facet | V. S. Mokeichev A. M. Sidorov |
| author_sort | V. S. Mokeichev |
| collection | DOAJ |
| description | In our previous articles, we introduced and explored the notion of φB -distributions with values in the Banach space. This offers a new perspective on the theory of solvability of linear problems, which is important for solving partial differential equations, especially equations with deviating arguments. Here, we provide an overview of the theory of such distributions, propose a new approach to justify the use of the Fourier method for solving linear problems, and write out a correctly solvable problem for a system of partial differential equations with deviating arguments. |
| first_indexed | 2024-03-07T23:46:50Z |
| format | Article |
| id | doaj.art-12b9067574f74c84a0ddd64108492ed5 |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-24T08:50:37Z |
| publishDate | 2023-11-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-12b9067574f74c84a0ddd64108492ed52024-04-16T11:42:17ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982023-11-011651688110.26907/2541-7746.2023.1.68-816Fourier method in the space of φB - distributionsV. S. Mokeichev0A. M. Sidorov1Kazan Federal UniversityKazan Federal UniversityIn our previous articles, we introduced and explored the notion of φB -distributions with values in the Banach space. This offers a new perspective on the theory of solvability of linear problems, which is important for solving partial differential equations, especially equations with deviating arguments. Here, we provide an overview of the theory of such distributions, propose a new approach to justify the use of the Fourier method for solving linear problems, and write out a correctly solvable problem for a system of partial differential equations with deviating arguments.https://uzakufismat.elpub.ru/jour/article/view/7differential equationfourier methodφb -distribution(φ, y, a, x)-solution |
| spellingShingle | V. S. Mokeichev A. M. Sidorov Fourier method in the space of φB - distributions Учёные записки Казанского университета. Серия Физико-математические науки differential equation fourier method φb -distribution (φ, y, a, x)-solution |
| title | Fourier method in the space of φB - distributions |
| title_full | Fourier method in the space of φB - distributions |
| title_fullStr | Fourier method in the space of φB - distributions |
| title_full_unstemmed | Fourier method in the space of φB - distributions |
| title_short | Fourier method in the space of φB - distributions |
| title_sort | fourier method in the space of φb distributions |
| topic | differential equation fourier method φb -distribution (φ, y, a, x)-solution |
| url | https://uzakufismat.elpub.ru/jour/article/view/7 |
| work_keys_str_mv | AT vsmokeichev fouriermethodinthespaceofphbdistributions AT amsidorov fouriermethodinthespaceofphbdistributions |