Approximation of functions subharmonic in a disk by the logarithm of the modulus of an analytic function

Abstract

Yulmukhametov's result concerning the approximation of a function subharmonic in a bounded domain by the logarithm of the modulus of an analytic function is supplemented with an estimate of the exceptional set in the important case of a disk. We show that this approximation is unimprovable in a certain sense.