A question by Alexei Aleksandrov and logarithmic determinants

الأصل · EN

We answer negatively to the question posed by Aleksandrov concerning analytic functions of Smirnov's class in the unit disk with pure imaginary boundary values. We also find new sufficient conditions for representations of functions of Smirnov's class by the Schwartz and Cauchy integrals. These conditions extend a previous result of Aleksandrov.