Nondeformed Generalized Dunkl Transform on the Line

A generalization of the Dunkl transform can be the -generalized Fourier transform, but it deforms good classes of functions, for example, the Schwartz space. In this paper, we study the nondeformed generalized Dunkl transform on the line. Two generalized translation operators are defined. Integral r...

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Bibliographic Details
Published in:Mathematical Notes 2023-10, Vol.114 (3-4), p.443-456
Main Author: Ivanov, V. I.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Fourier transforms
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary:A generalization of the Dunkl transform can be the -generalized Fourier transform, but it deforms good classes of functions, for example, the Schwartz space. In this paper, we study the nondeformed generalized Dunkl transform on the line. Two generalized translation operators are defined. Integral representations are obtained for them and -boundedness is proved. Two convolutions are defined for which the Young theorem is established. As an application, we study conditions for the -convergence of generalized means.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434623090171