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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {Description of {Unconditional} {Bases} {Formed} by {Values} of the {Dunkl} {Kernels}},
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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/

[1] C. F. Dunkel, Trans. Amer. Math. Soc., 311:1 (1989), 167–183 | DOI | MR

[2] M. de Jeu, Trans. Amer. Math. Soc., 358:10 (2006), 4225–4250 | DOI | MR | Zbl

[3] N. B. Anderson, M. de Jeu, Int. Math. Res. Notices, 30 (2005), 1817–1831 | DOI

[4] M. M. Dzhrbashyan, Integralnye preobrazoveniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966 | MR

[5] Dzh. Garnett, Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR

[6] G. M. Gubreev, Algebra i analiz, 12:6 (2000), 1–97 | MR

[7] G. M. Gubreev, Izv. RAN, ser. matem, 69:1 (2005), 17–60 | DOI | MR | Zbl

[8] B. Ya Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956