Abstract
In this paper, using a generalized translation operator, we obtain an analog of Younis’ theorem, [9, Theorem 5.2], for the Helgason Fourier transform of a set of functions satisfying the Dini–Lipschitz condition in the space
References
[1] Bray W. O. and Pinsky M. A., Growth properties of Fourier transforms via module of continuity, J. Funct. Anal. 255 (2008), no. 9, 2256–2285. Search in Google Scholar
[2] Helgason S., Differential Geometry and Symmetric Spaces (in Russian), Mir, Moscow, 1964. Search in Google Scholar
[3] Helgason S., A duality for symmetric spaces with applications to group representations, Adv. Math. 5 (1970), no. 1, 1–154. 10.1016/0001-8708(70)90037-XSearch in Google Scholar
[4] Helgason S., Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, 1978. Search in Google Scholar
[5] Helgason S., Groups and Geometric Analysis: Integral Geometry, Invariant Differential Operators, and Spherical Functions (in Russian), Mir, Moscow, 1987. Search in Google Scholar
[6] Helgason S., Geometric Analysis on Symmetric Spaces, American Mathematical Society, Providence, 1994. 10.1090/surv/039/02Search in Google Scholar
[7]
Platonov S. S.,
Approximation of functions in
[8] Platonov S. S., The Fourier transform of function satisfying the Lipshitz condition on rank 1 symetric spaces, Sib. Math. J. 46 (2005), no. 2, 1108–1118. 10.1007/s11202-005-0105-zSearch in Google Scholar
[9] Younis M. S., Fourier transforms of Dini–Lipschitz functions, Int. J. Math. Math. Sci. 9 (1986), no. 2, 301–312. 10.1155/S0161171286000376Search in Google Scholar
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Remark on Weil’s conjectures
- Characterization of Dini–Lipschitz functions for the Helgason Fourier transform on rank one symmetric spaces
- A note on the generic nature of Pringsheim functions
- Asymptotic analysis of a class of Ginzburg–Landau equations in thin multidomains
- Ulam–Hyers stabilities of a generalized composite functional equation in non-Archimedean spaces
- On the square subgroups of decomposable torsion-free abelian groups of rank three
Articles in the same Issue
- Frontmatter
- Remark on Weil’s conjectures
- Characterization of Dini–Lipschitz functions for the Helgason Fourier transform on rank one symmetric spaces
- A note on the generic nature of Pringsheim functions
- Asymptotic analysis of a class of Ginzburg–Landau equations in thin multidomains
- Ulam–Hyers stabilities of a generalized composite functional equation in non-Archimedean spaces
- On the square subgroups of decomposable torsion-free abelian groups of rank three