Carleman’s formula for $A(z)$-analytic functions

In the report we consider $A(z)$-analytic functions in the case when A(z) is an anti-analytic function. The report presents the $A(z)$-harmonic measure in the lemniscate, constructs a “quenching” function, and proves an analogue of the Carleman formula for $A(z)$-analytic functions.