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 …

We construct a two-parameter family of actions ωk, a of the Lie algebra 𝔰𝔩 (2, ℝ) by
differential–difference operators on ℝN∖{0}. Here k is a multiplicity function for the Dunkl …

In this paper, a family of radial deformations of the realization of the Lie superalgebra
$\mathfrak {osp}(1| 2) $ in the theory of Dunkl operators is obtained. This leads to a Dirac …

In this paper, a new method is developed to obtain explicit and integral expressions for the
kernel of the (κ, a)-generalized Fourier transform for κ= 0. In the case of dihedral groups, this …

For functions that take values in the Clifford algebra, we study the Clifford–Fourier transform
on \mathbbR^m defined with a kernel function K x,\y):=e^\mathrmiπ2\underliney{\mathrme …

The Howe dual pair allows the characterization of the classical Fourier transform (FT) on the
space of rapidly decreasing functions as the exponential of a well-chosen element of such …

Dunkl operators associated with finite reflection groups generate a commutative algebra of
differential-difference operators. There exists a unique linear operator called intertwining …

In this paper, Hermite polynomials related to quantum systems with orthogonal O (m)‐
symmetry, finite reflection group symmetry 𝒢< O (m), symplectic symmetry Sp (2n) and …

HARDY INEQUALITIES FOR FRACTIONAL (k, a)-GENERALIZED HARMONIC
OSCILLATOR II 1. Introduction In the last talk [21], we proved a H Page 1 HARDY …

sl 2 is generated by the super Laplace operator and the generalized norm squared. In this
paper, an inner product on superspace for which this representation is skew-symmetric is …