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...

We develop a framework for establishing the Law of Large Numbers eigenvalues in random matrix ensembles as size goes to infinity simultaneously with beta (inverse temperature) parameter going zero. Our approach is based on analysis (symmetric) Dunkl transform this regime. As an application we obtain LLN sums matrices inverse temperature 0. This results one-parameter family binary operations whi...

By using the symmetry of Dunkl Laplacian operator, we prove a sharp Shannon-type inequality and logarithmic Sobolev for transform. Combining these inequalities, obtain new, short proof Heisenberg-type uncertainty principles in setting. Moreover, by combining Nash’s inequality, Carlson’s Sobolev’s embedding theorems transform, new inequalities involving L∞-norm. Finally, Lp-spaces, from which de...

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...

We introduce multiple Wilson polynomials, which give a new example of multiple orthogonal polynomials (Hermite-Padé polynomials) of type II. These polynomials can be written as a Jacobi-Piñeiro transform, which is a generalization of the Jacobi transform for Wilson polynomials, found by T.H. Koornwinder. Here we need to introduce Jacobi and JacobiPiñeiro polynomials with complex parameters. Som...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

We introduce multiple Wilson polynomials, which give a new example of multiple orthogonal polynomials (Hermite-Padé polynomials) of type II. These polynomials can be written as a Jacobi-Piñeiro transform, which is a generalization of the Jacobi transform for Wilson polynomials, found by T.H. Koornwinder. Here we need to introduce Jacobi and JacobiPiñeiro polynomials with complex parameters. Som...