Geodesic
Nondeformed Generalized Dunkl transform on the Line
Matematičeskie zametki, Tome 114 (2023) no. 4, pp. 509-524

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A generalization of the Dunkl transform can be the $(k,a)$-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 $L_p$-boundedness is proved. Two convolutions are defined for which the Young theorem is established. As an application, we study conditions for the $L_p$-convergence of generalized means.
Keywords: generalized Fourier transform, generalized Dunkl transform, generalized translation operator, convolutions and generalized means. 
@article{MZM_2023_114_4_a2,
     author = {V. I. Ivanov},
     title = {Nondeformed {Generalized} {Dunkl} transform on the {Line}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {509--524},
     publisher = {mathdoc},
     volume = {114},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_4_a2/}
}
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V. I. Ivanov. Nondeformed Generalized Dunkl transform on the Line. Matematičeskie zametki, Tome 114 (2023) no. 4, pp. 509-524. http://geodesic.mathdoc.fr/item/MZM_2023_114_4_a2/