Solution of constraints of supergauge theory in the harmonic $SU(2)/U(1)$ superspace

The constraints for the components of the superfield connection of the analytic representation of supersymmetric $N=2$ gauge theory in the harmonic approach are solved. The solution is equivalent to the solution of Ogievetskii et al. An iterative expression is obtained for the action of the supergauge theory in the form of an integral over the complete $N=2$ superspace. The action density is expressed in terms of the logarithm of the determinant of a pseudodifferential operator that contains the operator of the basic covariant harmonic derivative.