On Fourier multipliers and absolute convergence of Fourier integrals of radial functions
We obtain sufficient conditions for the representability of a function in the form of an absolutely convergent Fourier integral. These conditions are given in terms of the joint behavior of the function and its derivatives at infinity, and their efficiency and exactness are verified with the use of...
Збережено в:
| Дата: | 2010 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2010
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2954 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We obtain sufficient conditions for the representability of a function in the form of an absolutely convergent Fourier integral. These conditions are given in terms of the joint behavior of the function and its derivatives at infinity, and their efficiency and exactness are verified with the use of a known example. We also consider radial functions of an arbitrary number of variables. |
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