Completeness and minimality of systems of Bessel functions

Abstract

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