In this article, we establish first a geometric Paley–Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the L p → L norm of Dunkl translations in dimension 1. Finally we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.

In this paper, we define subspaces of L by differences using the Dunkl translation operators that we call Besov-Dunkl spaces. We provide characterization of these spaces by the Dunkl convolution.

From the classical differential equation of Jacobi fields, one naturally defines the Jacobi operator of a Riemannian manifold with respect to any tangent vector. A straightforward computation shows that any real, complex and quaternionic space forms satisfy that any two Jacobi operators commute. In this way, we classify the real hypersurfaces in quaternionic projective spaces all of whose tange...

We exhibit several families of Jacobi–Videv pseudo-Riemannian manifolds which are not Einstein. We also exhibit Jacobi–Videv algebraic curvature tensors where the Ricci operator defines an almost complex structure.

We establish an integral representations of a right inverses of the Askey-Wilson finite difference operator in an L2 space weighted by the weight function of the continuous q-Jacobi polynomials. We characterize the eigenvalues of this integral operator and prove a q-analog of the expansion of eixy in Jacobi polynomials of argument x. We also outline a general procedure of finding integral repre...

We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be the spectra of two different self-adjoint extensions of a Jacobi operator in the limit circle case. Mathematics Subject Classification(2000): 47B36, 49N45, ...

In the framework of theory Dunkl-deformed bosons, Bose-Einstein condensation two and three-dimensional Dunkl-boson gases confined in one-dimensional gravitational field is investigated. Using semi-classical approximation method, we calculate expressions Dunkl-critical temperature $T_{c}^{D}$, ground state population $\frac{N_{0}^{D}}{N}$ Dunkl-mean energy Dunkl-specific heat functions. Further ...

Let (X, ω) be a symplectic orbifold which is locally like the quotient of a Z2 action on R . Let A ((~)) X be a deformation quantization of X constructed via the standard Fedosov method with characteristic class being ω. In this paper, we construct a universal deformation of the algebra A ((~)) X parametrized by codimension 2 components of the associated inertia orbifold X̃ . This partially conf...

An elementary non-technical introduction to group representations and orthogonal polynomials is given. Orthogonality relations for the spherical functions for the rotation groups in Euclidean space (ultraspherical polynomials), and the matrix elements of SU(2) (Jacobi polynomials) are discussed. A general theory for finite groups acting on graphs, giving a finite set of discrete orthogonal poly...

We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the Borg-Marchenko theorem for Schrödinger operators in the half-line. Furthermore, we give necessary and sufficient conditions for two real sequences to be the spectra of a Jacobi operator with different bou...