Geodesic
On the completeness and minimality of sets of Bessel functions in~weighted $L^2$-spaces
Eurasian mathematical journal, Tome 6 (2015) no. 1, pp. 123-131

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We establish a criterion for the completeness and minimality of the system $(x^{-p-1}\sqrt{x\rho_k}J_\nu(x\rho_k):k\in\mathbb{N})$ in the space $L^2((0;1); x^{2p}dx)$ where $J_\nu$ is the Bessel function of the first kind of index $\nu\geqslant1/2$, $p\in\mathbb{R}$ and $(\rho_k : k\in\mathbb{N})$ is a sequence of distinct nonzero complex numbers. 
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     author = {B. V. Vynnyts'kyi and R. V. Khats'},
     title = {On the completeness and minimality of sets of {Bessel} functions in~weighted $L^2$-spaces},
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B. V. Vynnyts'kyi; R. V. Khats'. On the completeness and minimality of sets of Bessel functions in~weighted $L^2$-spaces. Eurasian mathematical journal, Tome 6 (2015) no. 1, pp. 123-131. http://geodesic.mathdoc.fr/item/EMJ_2015_6_1_a9/