In this review, we give an overview of several recent generalizations of the Fourier transform,
related to either the Lie algebra or the Lie superalgebra. In the former case, one obtains …

The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a
Hamiltonian constructed from the combination of two independent parabosonic oscillators …

We present an exact solution of a confined model of the non-relativistic quantum harmonic
oscillator, where the effective mass and the angular frequency are dependent on the …

In this paper, we present the basic k-Hankel wavelet theory. Next, we study the
boundedness and compactness of localization operators associated with k-Hankel wavelet …

Two Dunkl oscillator models are considered: one singular and the other with a 2: 1
frequency ratio. These models are defined by Hamiltonians which include the reflection …

We introduce the notion of the (k, a)-generalized wavelet transform. Particular cases of such
generalized wavelet transform are the classical and the Dunkl wavelet transforms. The …

A Hopf algebra with four generators among which an involution (reflection) operator, is
introduced. The defining relations involve commutators and anticommutators. The discrete …

Abstract The Bannai-Ito algebra is presented together with some of its applications. Its
relations with the Bannai-Ito polynomials, the Racah problem for the sl− 1 (2) algebra, a …

A one-parameter family of operators that have the complementary Bannai-Ito (CBI)
polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of …

We constructed a new model of the non-relativistic quantum harmonic oscillator within the
canonical approach. It is asymmetrically confined into the infinitely high potential well …