our aim in this paper is to prove an analog of younis's theorem on the image under the jacobi transform of a class functions satisfying a generalized dini-lipschitz condition in the space $mathrm{l}_{(alpha,beta)}^{p}(mathbb{r}^{+})$, $(1< pleq 2)$. it is a version of titchmarsh's theorem on the description of the image under the fourier transform of a class of functions satisfying the dini-lip...

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

We prove an addition formula for Jacobi functions r ~' ~) (~17_~-~ ) analogous to the known addition formula for Jacobi polynomials. We exploit the positivity of the coefficients in the addition formula by giving the following application. We prove that the product of two Jacobi functions of the same argument has a nonnegative Fourier-Jacobi transform. This implies that the convolution structur...

Let Hg and Dg be the Siegel upper half plane and the generalized unit disk of degree g respectively. Let C be the Euclidean space of all h× g complex matrices. We present a partial Cayley transform of the Siegel-Jacobi disk Dg × C (h,g) onto the Siegel-Jacobi space Hg × C (h,g) which gives a partial bounded realization of Hg × C (h,g) by Dg ×C . We prove that the natural actions of the Jacobi g...

Recently, the continuous Jacobi transform and its inverse are defined and studied in [i] and [2]. In the present work, the transform is used to derive a series representation for the Jacobi functions Pe’) (x) -% -1/2. The case e = =0 yields a representation for the Legendre functions and has been dealt with zn [3]. When I is a positive integer n, the representation redu...