Abstract. We give a detailed description of the resolution of the identity of a second order q-difference operator considered as an unbounded self-adjoint operator on two different Hilbert spaces. The q-difference operator and the two choices of Hilbert spaces naturally arise from harmonic analysis on the quantum group SUq(1, 1) and SUq(2). The spectral analysis associated to SUq(1, 1) leads to...

This paper studies the optimal investment problem of utility maximization with taxes, dividends and transaction costs under the constant elasticity of variance (CEV) model. The Hamilton-Jacobi-Bellman (HJB) equation associated with the optimization problem is established via stochastic control approach. Applying power transform and variable change technique, we obtain explicit solutions for the...

We use the well-known observation that solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algorithm for computing multi-dimensional Jacobi polynomial transforms. More explicitly, it follows from this matrix corresponding discrete transform is Hadamard product numerically low-rank Fourier (DFT) matrix. The applicatio...

In this work, we are interested by the q-Bessel Fourier transform with a new approach. Many important results of this q-integral transform are proved with a new constructive demonstrations and we establish in particular the associated q-Fourier-Neumen expansion which involves the q-little Jacobi polynomials.

In this work, we are interested by the q-Bessel Fourier transform with a new approach. Many important results of this q-integral transform are proved with a new constructive demonstrations and we establish in particular the associated q-Fourier-Neumen expansion which involves the q-little Jacobi polynomials.

A series expansion for Heckman-Opdam hypergeometric functions φλ is obtained for all λ ∈ a∗ C . As a consequence, estimates for φλ away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the no...

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...

In this paper, we introduce the notion of Dunkl-classical orthogonal polynomials. Then, we show that generalized Hermite and generalized Gegenbauer polynomials are the only Dunkl-classical symmetric orthogonal polynomials by solving a suitable differential-difference equation. 2006 Elsevier Inc. All rights reserved.