On the growth of ridge functions non-vanishing in an angular domain

Abstract

For an entire ridge function of finite order $\rho$ which is non-vanishing in the angle $\{z : |\arg z - \pi/2| < \alpha \} \cup \{z : |argz + \pi/2| < \alpha \}$, $0 < \alpha \le \pi/2$, the sharp estimate of $\rho $ in terms of $\alpha $ is obtained. Analogous result is obtained for ridge functions analytic in the upper half-plane.