The Dunkl transform is an integral transform on R" which generalises the classical Fourier transform. On suitable function spaces, it establishes a natural correspondence between the action of multiplication operators on one hand and so-called Dunkl operators on the other. These are differential-difference operators, generalising the usual partial derivatives, which are associated with a finite...

This paper presents a series of applications of the Jacobi evolution equations along geodesics in groups of diffeomorphisms. We describe, in particular, how they can be used to perform implementable gradient descent algorithms for image matching, in several situations, and illustrate this with 2D and 3D experiments. We also discuss parallel translation in the group, and its projection on shape ...

A new family of AN -type Dunkl operators preserving a polynomial subspace of finite dimension is constructed. Using a general quadratic combination of these operators and the usual Dunkl operators, several new families of exactly and quasi-exactly solvable quantum spin Calogero–Sutherland models are obtained. These include, in particular, three families of quasi-exactly solvable elliptic spin H...

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...

For a better understanding of the physical systems, even at quantum level, thermal quantities can be investigated. Recently, we realized that parity system also examined simultaneously, by substituting Dunkl operator with ordinary differential in mechanics. In this manuscript, consider two relativistic Dunkl-oscillators and investigate their well-known statistical methods. Besides, establish re...

The Jacobi-Stirling numbers of the first and second kind were introduced in 2007 by Everitt et al. In this article we find new explicit formulas for Jacobi Stirling numbers. Furthermore, derive study class so-called generalized Some special cases such as Legendre-Stirling are given. interesting combinatorial identities obtained.

We report on a parallel implementation of the Jacobi–Davidson (JD) to compute a few eigenpairs of a large real symmetric generalized matrix eigenvalue problem

With the aid of symbolic computation, a new extended Jacobi elliptic function expansionmethod is presented by means of a new ansatz, in which periodic solutions of nonlinear evolution equations, which can be expressed as a finite Laurent series of some 12 Jacobi elliptic functions, are very effective to uniformly construct more new exact periodic solutions in terms of Jacobi elliptic function s...

We derive explicitly the weights and the nodes of the generalized Gauss-Radau and Gauss-Lobatto quadratures with Jacobi weight functions. AMS subject classification: 65D32, 65D30, 41A55.

Abstract It is shown that the extensions of exactly-solvable quantum mechanical problems connected with replacement ordinary derivatives by Dunkl ones and classical orthogonal polynomials exceptional can be easily combined. For such a purpose, example oscillator on line considered three different types rationally-extended oscillators are constructed. The corresponding wavefunctions expressed in...