‎In this paper‎, ‎using a generalized translation operator‎, ‎we obtain a generalization of Younis Theorem 5.2 in [3] for the Cherednik-Opdam transform for functions satisfying the $(delta,gamma,p)$-Cherednik-Opdam Lipschitz condition in the space‎ ‎$L^{p}_{alpha,beta}(mathbb{R})$.

Consider a root system of type BC1 on the real line R with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an L-space on R to a L-space of C-valued functions on R with the Harish-Chandra measure |c(λ)|dλ. By introducing a weight function of the form cosh(t) tanh t on R we find an orthogonal basis for the L-space on R consisting of even and odd func...

We find a biorthogonal expansion of the Cayley transform of the non-symmetric Jack functions in terms of the non-symmetric Jack polynomials, the coefficients being Meixner–Pollaczek type polynomials. This is done by computing the Cherednik–Opdam transform of the non-symmetric Jack polynomials multiplied by the exponential function.

In this paper, we study several weighted norm inequalities for the Opdam–Cherednik transform. We establish different versions of Heisenberg–Pauli–Weyl inequality particular, give an extension using weights with exponents and present a variation that incorporates [Formula: see text]-norms Also, prove version Hardy–Littlewood Finally, other variations such as Nash-type Clarkson-type

In this paper, we study a few versions of the uncertainty principle for windowed Opdam–Cherednik transform. particular, establish orthonormal sequences, Donoho–Stark's principle, Benedicks‐type Heisenberg‐type and local inequality We also obtain using ‐entropy

The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces associated with transform. In particular, we obtain Cowling–Price's, Hardy's and Morgan's spaces. proofs results are based versions Phragmén–Lindlöf type result several complex variables properties Gaussian kernel Jacobi–Cherednik operator.

In this paper, we introduce the Hausdorff operator associated with Opdam--Cherednik transform and study boundedness of in various Lebesgue spaces. particular, prove spaces, grand quasi-Banach spaces that are transform. Also, give necessary sufficient conditions for these

In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on symbol $\varsigma$ and two windows functions $g_1$ $g_2$. We first present some basic properties the windowed Opdam-Cherednik transform. Then, use modulation spaces associated with transform appropriate classes for symbols windows, boundedness compactness spaces. Final...

In this note, a new proof for the positivity of Dunkl’s intertwining operator in the crystallographic case is given. It is based on an asymptotic relationship between the Opdam-Cherednik kernel and the Dunkl kernel as recently observed by M. de Jeu, and on positivity results of S. Sahi for the Heckman-Opdam polynomials and their nonsymmetric counterparts. 2000 AMS Subject Classification: 33C52,...