Dunkl operators associated with finite reflection groups generate a commutative algebra of differential-difference operators. There exists unique linear operator called intertwining which intertwines between this and the standard differential also generalization Fourier transform in context transform. In paper, we determine an integral expression for kernel, is kernel transform, all dihedral gr...

We introduce an algebra H consisting of difference-reflection operators and multiplication operators that can be considered as a q = 1 analogue of Sahi's double affine Hecke algebra related to the affine root system of type (C ∨ 1 , C1). We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra H, and the corresponding Fourier transforms. These eigenfunctions are non-symmetric v...

Abstract. Integrability, algebraic structures and orthogonal basis of the Calogero model are studied by the quantum Lax and Dunkl operator formulations. The commutator algebra among operators including conserved operators and creation-annihilation operators has the structure of the W-algebra. Through an algebraic construction of the simultaneous eigenfunctions of all the commuting conserved ope...

Abstract Some examples of Appell–Dunkl sequences are shown using determined operators. Specifically, whose generating functions the form $$E_{\alpha }(xt)/(1\pm t^m)$$ E α ( x t ) /</...

the main purpose of this paper is to detemine the fine spectrum of the generalized difference operator delta_{uv} over the sequence space c0. these results are more general than the fine spectrum of the generalized difference operator delta_{uv} of srivastava and kumar.

We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...

We give some interest in radial Dunkl processes associated with dihedral systems. We write down the semi group density and as a by-product the generalized Bessel function and the W -invariant generalized Hermite polynomials. Then, a skew product decomposition, involving only independent Bessel processes, is given and the tail distribution of the first hitting time of boundary of the Weyl chambe...

We study an extension of the classical Paley-Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and FourierNeumann type series as special cases. Concerning applications, several new results are obtained. From the Dunkl analogue of Gegenbauer’s expansion of the plane wave, we ...