Spherical Transformation of Generalized Poisson Shift and Properties of Weighted Lebesgue Classes of Functions
- Авторы: Lyakhov L.1, Roshchupkin S.2, Sanina E.1
-
Учреждения:
- Voronezh State University
- I. A. Bunin Elets State University
- Выпуск: Том 224, № 5 (2017)
- Страницы: 699-708
- Раздел: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239669
- DOI: https://doi.org/10.1007/s10958-017-3445-x
- ID: 239669
Цитировать
Аннотация
We obtain a formula for the spherical transformation of generalized shift of a function depending on multiple-axial spherical symmetry. This formula shows that the generalized shift order depends on the dimension of the spherically symmetric part of the Euclidean space. The formula can be used for reducing some problems in weighted function spaces to the case of function spaces without weight. For an example we prove the global continuity with respect to shift and show that functions of class \( {C_{ev}^{\infty}}_{,0} \) are dense in the weighted Lebesgue classes.
Об авторах
L. Lyakhov
Voronezh State University
Автор, ответственный за переписку.
Email: levnlya@mail.ru
Россия, 1, Universitetskaya pl, Voronezh, 394006
S. Roshchupkin
I. A. Bunin Elets State University
Email: levnlya@mail.ru
Россия, 28, Kommunarov Str., Lipetskaya obl., Elets, 399770
E. Sanina
Voronezh State University
Email: levnlya@mail.ru
Россия, 1, Universitetskaya pl, Voronezh, 394006