**N. Khatiashvili**

## Inversion of the Cauchy Integral Taken over the
Double Periodic Line

**abstract:**

The Cauchy type singular integral equation is investigated when the line of
integration is the union of a countable number of disconnected segments. The
equation is equivalently reduced to an equation with double periodic kernel.
Effective solutions having integrable singularities at the end-points of the
line of integration are obtained.