Let $ G $ be a convex domain with exactly one singular point $ z_{s} $ of an analytic function $ Q(z) $ , symmetric with respect to this point.For large values of the modulus of the spectral parameter $ \rho $ , we study the asymptotics of the transfer matrix $ P $ of the Sturm–Liouville equation with potential $ Q $ along an arbitrary curve lying in the domain $ G $ and not passing through the point $ z_{s} $ .Necessary and sufficient conditions are given under which the matrix $ P $ is independent of the parameter $ \rho $ , and its structure is described in this case.In all other cases, we prove that every entry of the transfer matrix is an entire function of $ \rho $ of completely regular growth of order $ 1/2 $ , with the same piecewise trigonometric indicator and angular density of zeros.Formulas for these characteristics are obtained for three possible types.
