Differential equations on complex manifolds

In the paper under review, the authors study the linear partial differential equations with constant coefficients on the complex manifold {Bbb C}^n. Using the Stern-Shatalov integral transform the authors solve the complex Cauchy problem. Then the authors consider two applications: describe the singularities of the solution of the Cauchy problem and solve a physical problem of sweeping the charge inside the domain (balayage inwards problem).