Unconditional bases of systems of Bessel functions

We find a criterion of unconditional basicity of the system $(\sqrt{x\rho_k}J_\nu(x\rho_k): k\in\mathbb{N})$ in the space $L^2(0; 1)$ where $J_\nu$ is the Bessel function of the first kind of index $\nu\geqslant-1/2$ and $(\rho_k: k\in\mathbb{N})$ is a sequence of distinct nonzero complex numbers.