  The existence of magnetohydrodynamic mean-field alpha^2-dynamos with
spherically symmetric, isotropic helical turbulence function alpha is related
to a non-self-adjoint spectral problem for a coupled system of two singular
second order ordinary differential equations. We establish global estimates for
the eigenvalues of this system in terms of the turbulence function alpha and
its derivative alpha'. They allow us to formulate an anti-dynamo theorem and a
non-oscillation theorem. The conditions of these theorems, which again involve
alpha and alpha', must be violated in order to reach supercritical or
oscillatory regimes.
