Geodesic
Completeness and minimality of systems of Bessel functions
Ufa mathematical journal, Tome 5 (2013) no. 2, pp. 131-141

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We find the necessary and sufficient conditions for the completeness and minimality in the space $L^2(0;1)$ of system $(\sqrt{x\rho_k}J_{\nu}(x\rho_k):k\in\Bbb N)$ generated by Bessel function of the first kind of index $\nu\ge -1/2$. Moreover, we establish a criterion for the completeness and minimality of system $(x^{-2}\sqrt{x\rho_k}J_{3/2}(x\rho_k):k\in\Bbb N)$ in the space $L^2((0;1);x^2 dx)$.
Keywords: Paley–Wiener theorem, Bessel function, entire function, complete system, minimal system, basis.
Mots-clés : biorthogonal system 
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     author = {B. V. Vynnyts'kyi and R. V. Khats'},
     title = {Completeness and minimality of systems  of {Bessel} functions},
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B. V. Vynnyts'kyi; R. V. Khats'. Completeness and minimality of systems  of Bessel functions. Ufa mathematical journal, Tome 5 (2013) no. 2, pp. 131-141. http://geodesic.mathdoc.fr/item/UFA_2013_5_2_a10/