On the growth of a subharmonic function with Riesz' measure on a ray

We consider functions $v$ subharmonic in $\mathbf R^n$, $n\ge2$, which are natural counterparts of Weierstrass canonical products (so-called Weierstrass canonical integrals). Under assumptions that the order of $v$ is a noninteger number and the Riesz measure of $v$ is supported by a ray we obtain sharp estimates of asymptotical behavior of $v$ at infinity along rays.