Relationship between manifolds of solutions to generic and model generalized Cauchy-Riemann systems with a singular point

Abstract

The unique solvability of a specific two-dimensional integral equation is proved. It is used to establish a one-to-one correspondence between the sets of continuous solutions to two systems of the form$2\overline z \partial _{\overline z } w - b(z)\overline w = 0$ and$2\overline z \partial _{\overline z } \Phi - b(0)\overline \Phi = 0$ defined in the same domainG (z=0∈G).