### Non-local boundary value problem for partial differential equation in a complex domain

#### Abstract

The paper is devoted to the investigation of a non-local boundary value problem for partial differential equations with the operator of the generalized differentiation $B=z\frac{\partial}{\partial z}$, which operate on functions of scalar complex variable $z$. The unity theorem and existence theorems of the solution of problem in the space $\mathbf{H}_{q}^n(\mathcal{D})$ are proved. Correctness after Hadamard of the problem is shown. It distinguishes her from an ill-conditioned after Hadamard problem with many spatial variables.

#### Keywords

partial differential equation, operator of generalized differentiation, generalized functions, discriminant of the polynomial, small denominators

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