The Fourier Transform Associated to the k-Hyperbolic Dirac Operator

The polynomial null solutions of the k -hyperbolic Dirac operator are investigated by the osp ( 1 | 2 ) approach. These solutions are then utilized to construct the (fractional) Fourier transform associated to the k -hyperbolic Dirac operator. The resulting integral kernels are found to be a specifi...

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Bibliographic Details
Published in:Advances in applied Clifford algebras 2023-07, Vol.33 (3), Article 26
Main Authors: Li, Wenxin, Lian, Pan
Format: Article
Language:English
Subjects:
Applications of Mathematics
Fourier transforms
Inequalities
Kernels
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Polynomials
Theoretical
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Summary:The polynomial null solutions of the k -hyperbolic Dirac operator are investigated by the osp ( 1 | 2 ) approach. These solutions are then utilized to construct the (fractional) Fourier transform associated to the k -hyperbolic Dirac operator. The resulting integral kernels are found to be a specific kind of Dunkl kernels. Additionally, we give tight uncertainty inequalities for three distinct fractional Fourier transforms that we have defined. These inequalities are new even for the ordinary fractional Hankel and Weinstein transforms.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-023-01274-y