TY - JOUR
T1 - Dunkl operators and a family of realizations of osp(1|2)
AU - de Bie, H.
AU - Ørsted, B.
AU - Somberg, P.
AU - Souček, V.
N1 - Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012
Y1 - 2012
N2 - In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects of this operator are studied, such as the associated measure, the related Laguerre polynomials and the related Fourier transform. For special values of the parameters, it is possible to construct the kernel of the Fourier transform explicitly, as well as the related intertwining operator.
AB - In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects of this operator are studied, such as the associated measure, the related Laguerre polynomials and the related Fourier transform. For special values of the parameters, it is possible to construct the kernel of the Fourier transform explicitly, as well as the related intertwining operator.
UR - http://www.scopus.com/inward/record.url?scp=84859028052&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-2012-05608-X
DO - 10.1090/S0002-9947-2012-05608-X
M3 - Journal article
AN - SCOPUS:84859028052
SN - 0002-9947
VL - 364
SP - 3875
EP - 3902
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 7
ER -