DUNKL OPERATORS AND A FAMILY OF REALIZATIONS OF osp(1|2)

DUNKL OPERATORS AND A FAMILY OF REALIZATIONS OF osp(1|2)

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...

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Veröffentlicht in:Transactions of the American Mathematical Society 2012-07, Vol.364 (7), p.3875-3902
Hauptverfasser: DE BIE, H., ØRSTED, B., SOMBERG, P., SOUČEK, V.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Eigenfunctions
Fourier transformations
Harmonic analysis
Laplace transformation
Mathematical functions
Mathematical vectors
Polynomials
Scalars
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Zusammenfassung: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-2012-05608-X