Complete Radon–Kipriyanov Transform: Some Properties
- Авторы: Lyakhov L.1, Lapshina M.2, Roshchupkin S.3
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Учреждения:
- Voronezh State University
- Lipetsk State Pedagogical University
- Bunin Yelets State University
- Выпуск: Том 100, № 3 (2019)
- Страницы: 524-528
- Раздел: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225736
- DOI: https://doi.org/10.1134/S1064562419060061
- ID: 225736
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Аннотация
The even Radon–Kipriyanov transform (Kγ-transform) is suitable for studying problems with the Bessel singular differential operator \({{B}_{{{{\gamma }_{i}}}}} = \frac{{{{\partial }^{2}}}}{{\partial x_{i}^{2}}} + \frac{{{{\gamma }_{i}}}}{{{{x}_{i}}~}}\frac{\partial }{{\partial {{x}_{i}}}},{{\gamma }_{i}} > 0\). In this work, the odd Radon–Kipriyanov transform and the complete Radon–Kipriyanov transform are introduced to study more general equations containing odd B-derivatives \(\frac{\partial }{{\partial {{x}_{i}}}}~B_{{{{\gamma }_{i}}}}^{k},~~k = 0, 1, 2,~ \ldots \) (in particular, gradients of functions). Formulas of the Kγ-transforms of singular differential operators are given. Based on the Bessel transforms introduced by B.M. Levitan and the odd Bessel transform introduced by I.A. Kipriyanov and V.V. Katrakhov, a relationship of the complete Radon–Kipriyanov transform with the Fourier transform and the mixed Fourier–Levitan–Kipriyanov–Katrakhov transform is deduced. An analogue of Helgason’s support theorem and an analog of the Paley–Wiener theorem are given.
Об авторах
L. Lyakhov
Voronezh State University
Автор, ответственный за переписку.
Email: levnlya@mail.ru
Россия, Voronezh, 394018
M. Lapshina
Lipetsk State Pedagogical University
Автор, ответственный за переписку.
Email: marina.lapsh@yandex.ru
Россия, Lipetsk, 398020
S. Roshchupkin
Bunin Yelets State University
Автор, ответственный за переписку.
Email: roshupkinsa@mail.ru
Россия, Yelets, Lipetsk Region, 399770