Ufa Mathematical Journal
    Volume 5, Number 2, pp. 131-141

    Completeness and minimality of systems of Bessel functions

    Khats' R.V., Vynnyts'kyi B.V.


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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 $L^2((0;1);x^2 dx)$.