GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE DUNKL TRANSFORM IN THE SPACE $L^P(R)$
محورهای موضوعی : فصلنامه ریاضی
Elhamma Mohamed
1
(
)
Hind Lahlai
2
(
)
Radouan Daher
3
(
)
کلید واژه: Dunkl operator, Dunkl transform, generalized translation Dunkl operator,
چکیده مقاله :
In this paper, using a generalized Dunkl translation operator, we obtain a generalization of Titchmarsh's Theorem for the Dunkl transform for functions satisfying the$(\psi,p)$-Lipschitz Dunkl condition in the space $\mathrm{L}_{p,\alpha}=\mathrm{L}^{p}(\mathbb{R},|x|^{2\alpha+1}dx)$, where $\alpha>-\frac{1}{2}$.