On the solvability of one boundary value problem for polynomial differential operator in the class of functions of exponential type

The work is devoted to the problem of existence of global analytical solutions of the generalized Cauchy problem with initial-boundary conditions of Riquier type, specified on the coordinate hyperplanes. Used as the classic methods of complex analysis, and relatively new methods of the theory of amoebas algebraic hyperplanes. The authors prove the solvability of value problem in the class of functions of exponential type boundary for polynomial differential operator with constant coefficients and reveal the linear connection of the characteristics of the growth of solutions of boundary-value problem from the growth of the boundary conditions and right-hand side of the equation. Research methods can be useful for further research of the theory of differential operators.