Abstract The main aim of this article is to study a new generalizations the Gauss hypergeometric matrix and confluent functions by using two-parameter Mittag–Leffler function. In particular, we investigate certain important properties these extended such as integral representations, differentiation formulas, beta transform, Laplace transform. Furthermore, introduce an extension Jacobi orthogona...

We introduce and study a class of analytic difference operators admitting reflectionless eigenfunctions. Our construction of the class is patterned after the Inverse Scattering Transform for the reflectionless self-adjoint Schrödinger and Jacobi operators corresponding to KdV and Toda lattice solitons.

We consider the standard hypergeometric differential operator $\mathcal D$ regarded as an on complex plane $\mathbb C$ and conjugate $\bar{\mathcal D}$. These operators formally commute are adjoint one to another with respect appropriate weight. find conditions when they in Nelson sense write explicitly their joint spectral decomposition. It is determined by a two-dimensional counterpart of Jac...

Let Sp(n,R) be the symplectic group, and K∗ n its maximal compact subgroup. Then G = Sp(n,R)/K∗ n can be realized as the Siegel domain of type one. The square-integrable representation of G gives the admissible wavelets AW and wavelet transform. The characterization of admissibility condition in terms of the Fourier transform is given. The Bergman kernel follows from the viewpoint of coherent s...

In this paper, using a generalized Jacobi-Dunkl translation operator, we prove a generalization of Titchmarsh’s theorem for functions in the k-JacobiDunkl-Lipschitz class defined by the finite differences of order k ∈ N∗ and Sobolev spaces associated with the Jacobi-Dunkl operator.

Certain objects of conformal field theory, for example partition functions on the rectangle and torus, one-point are either invariant or transform simply under modular group, properties which should be preserved $T\overline T$ deformation. The formulation proof this statement in fact extents to more general such as deformed Jacobi forms. We show that deformation acts their Mellin transform, mul...

Abstract. We introduce a spectral transform for the finite relativistice Toda lattice (RTL) in generalized form. In the nonrelativistic case, Moser constructed a spectral transform from the spectral theory of symmetric Jacobi matrices. Here we use a nonsymmetric generalized eigenvalue problem for a pair of bidiagonal matrices (L, M) to define the spectral transform for the RTL. The inverse spec...

We devise a framework encompassing the classical theory of characteristics and the theory valid in the convex case recently obtained by R.T. Rockafellar and P. Wolenski. It relies on a notion of transform introduced by I. Ekeland. It involves a class of functions called Ekeland functions which is large enough to encompass convex functions, concave functions and linear-quadratic functions, as we...