Geodesic
Description of Unconditional Bases Formed by Values of the Dunkl Kernels
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 1, pp. 79-82

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Unconditional bases of the form $\{d_\alpha(i\lambda_n t): \lambda_n \in \Lambda\}$ in the space $L_2(-a, a)$ with measure $|x|^\gamma dx$, $\gamma=2\alpha+1$, are described. Here $d_\alpha(ixt)$ is the Dunkl kernel determined by $$ d_\alpha(z)=2^\alpha\Gamma(\alpha+1)z^{-\alpha}(J_\alpha(z)+iJ_{\alpha+1}(z)), \; \alpha>-1, $$ where $J_\alpha$ is the Bessel function of the first kind.
Keywords: Dunkl transform, unconditional basis, non-self-adjoint operator, entire function. 
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     author = {G. M. Gubreev and V. N. Levchuk},
     title = {Description of {Unconditional} {Bases} {Formed} by {Values} of the {Dunkl} {Kernels}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {79--82},
     publisher = {mathdoc},
     volume = {49},
     number = {1},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2015_49_1_a7/}
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G. M. Gubreev; V. N. Levchuk. Description of Unconditional Bases Formed by Values of the Dunkl Kernels. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 1, pp. 79-82. http://geodesic.mathdoc.fr/item/FAA_2015_49_1_a7/