On the polyconvolution for the Fourier cosine, Fourier sine, and Kontorovich–Lebedev integral transforms
The polyconvolution $∗_1(f,g,h)(x)$ of three functions $f, g$ and $h$ is constructed for the Fourier cosine $(F_c)$, Fourier sine $(F_s)$, and Kontorovich–Lebedev $(K_{iy})$ integral transforms whose factorization equality has the form $$F_c(∗_1(f,g,h))(y)=(F_sf)(y).(F_sg)(y).(K_{iy}h)\;\;∀y>...
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| Дата: | 2010 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2010
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2963 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | The polyconvolution $∗_1(f,g,h)(x)$ of three functions $f, g$ and $h$ is constructed for the Fourier cosine $(F_c)$, Fourier sine $(F_s)$, and Kontorovich–Lebedev $(K_{iy})$ integral transforms whose factorization equality has the form
$$F_c(∗_1(f,g,h))(y)=(F_sf)(y).(F_sg)(y).(K_{iy}h)\;\;∀y>0.$$
The relationships between this polyconvolution, the Fourier convolution, and the Fourier cosine convolution are established. In addition, we also establish the relationships between the product of the new polyconvolution and the products of the other known types of convolutions. As an application, we consider a class of integral equations with Toeplitz and Hankel kernels whose solutions can be obtained with the help of the new polyconvolution in the closed form. We also present the applications to the solution of systems of integral equations. |
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